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</div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Kerala school of astronomy and mathematics</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 17 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-17" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">17 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AF%D8%B1%D8%B3%D8%A9_%D9%83%D9%8A%D8%B1%D9%84%D8%A7_%D9%84%D8%B9%D9%84%D9%85_%D8%A7%D9%84%D9%81%D9%84%D9%83_%D9%88%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA" title="مدرسة كيرلا لعلم الفلك والرياضيات – Arabic" lang="ar" hreflang="ar" data-title="مدرسة كيرلا لعلم الفلك والرياضيات" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Escuela_de_Kerala" title="Escuela de Kerala – Spanish" lang="es" hreflang="es" data-title="Escuela de Kerala" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89cole_du_Kerala" title="École du Kerala – French" lang="fr" hreflang="fr" data-title="École du Kerala" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Escola_de_Kerala" title="Escola de Kerala – Galician" lang="gl" hreflang="gl" data-title="Escola de Kerala" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%BC%80%EB%9E%84%EB%9D%BC_%ED%95%99%ED%8C%8C" title="케랄라 학파 – Korean" lang="ko" hreflang="ko" data-title="케랄라 학파" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A5%87%E0%A4%B0%E0%A4%B2%E0%A5%80%E0%A4%AF_%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4_%E0%A4%B8%E0%A4%AE%E0%A5%8D%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%A6%E0%A4%BE%E0%A4%AF" title="केरलीय गणित सम्प्रदाय – Hindi" lang="hi" hreflang="hi" data-title="केरलीय गणित सम्प्रदाय" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Mazhab_astronomi_dan_matematika_Kerala" title="Mazhab astronomi dan matematika Kerala – Indonesian" lang="id" hreflang="id" data-title="Mazhab astronomi dan matematika Kerala" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Scuola_del_Kerala" title="Scuola del Kerala – Italian" lang="it" hreflang="it" data-title="Scuola del Kerala" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B5%87%E0%B4%B0%E0%B4%B3%E0%B5%80%E0%B4%AF%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4_%E0%B4%B8%E0%B4%B0%E0%B4%A3%E0%B4%BF" title="കേരളീയഗണിത സരണി – Malayalam" lang="ml" hreflang="ml" data-title="കേരളീയഗണിത സരണി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%B1%E3%83%BC%E3%83%A9%E3%83%A9%E5%AD%A6%E6%B4%BE" title="ケーララ学派 – Japanese" lang="ja" hreflang="ja" data-title="ケーララ学派" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Kerala-skolen_for_astronomi_og_matematikk" title="Kerala-skolen for astronomi og matematikk – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Kerala-skolen for astronomi og matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Escola_de_Querala_de_Astronomia_e_Matem%C3%A1tica" title="Escola de Querala de Astronomia e Matemática – Portuguese" lang="pt" hreflang="pt" data-title="Escola de Querala de Astronomia e Matemática" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9A%D0%B5%D1%80%D0%B0%D0%BB%D1%8C%D1%81%D0%BA%D0%B0%D1%8F_%D1%88%D0%BA%D0%BE%D0%BB%D0%B0_%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D0%B8_%D0%B8_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B8" title="Керальская школа астрономии и математики – Russian" lang="ru" hreflang="ru" data-title="Керальская школа астрономии и математики" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AF%87%E0%AE%B0%E0%AE%B3_%E0%AE%B5%E0%AE%BE%E0%AE%A9%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%AE%E0%AE%B1%E0%AF%8D%E0%AE%B1%E0%AF%81%E0%AE%AE%E0%AF%8D_%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_%E0%AE%AA%E0%AE%B3%E0%AF%8D%E0%AE%B3%E0%AE%BF" title="கேரள வானியல் மற்றும் கணிதவியல் பள்ளி – Tamil" lang="ta" hreflang="ta" data-title="கேரள வானியல் மற்றும் கணிதவியல் பள்ளி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Kerala_astronomi_ve_matematik_okulu" title="Kerala astronomi ve matematik okulu – Turkish" lang="tr" hreflang="tr" data-title="Kerala astronomi ve matematik okulu" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D0%B5%D1%80%D0%B0%D0%BB%D1%8C%D1%81%D1%8C%D0%BA%D0%B0_%D1%88%D0%BA%D0%BE%D0%BB%D0%B0_%D0%B0%D1%81%D1%82%D1%80%D0%BE%D0%BD%D0%BE%D0%BC%D1%96%D1%97_%D1%82%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B8" title="Керальська школа астрономії та математики – Ukrainian" lang="uk" hreflang="uk" data-title="Керальська школа астрономії та математики" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Tr%C6%B0%E1%BB%9Dng_ph%C3%A1i_Kerala" title="Trường phái Kerala – Vietnamese" lang="vi" hreflang="vi" data-title="Trường phái Kerala" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" 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and Mathematics">Kerala School of Astronomy and Mathematics</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Hindu astronomy, mathematics, science school in India</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><style data-mw-deduplicate="TemplateStyles:r1256395774">.mw-parser-output .ib-school .infobox-header,.mw-parser-output .ib-school .infobox-above{background:lavender;color:#202122}.mw-parser-output .ib-school .infobox-image .logo,.mw-parser-output .ib-school .infobox-image .seal{background-color:#f8f9fa}</style><table class="infobox vcard ib-school"><tbody><tr><th colspan="2" class="infobox-above fn org notheme">Kerala school of astronomy and mathematics</th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Kerala_school_chain_of_teachers.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Kerala_school_chain_of_teachers.jpg/250px-Kerala_school_chain_of_teachers.jpg" decoding="async" width="250" height="190" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Kerala_school_chain_of_teachers.jpg/375px-Kerala_school_chain_of_teachers.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Kerala_school_chain_of_teachers.jpg/500px-Kerala_school_chain_of_teachers.jpg 2x" data-file-width="2193" data-file-height="1668" /></a></span><div class="infobox-caption">Chain of teachers of the Kerala school</div></td></tr><tr><th colspan="2" class="infobox-header notheme">Location</th></tr><tr class="adr"><td colspan="2" class="infobox-full-data"><div style="display:inline;" class="street-address">Central and Northern <a href="/wiki/Kerala" title="Kerala">Kerala</a>, India</div></td></tr><tr><th colspan="2" class="infobox-header notheme">Information</th></tr><tr><th scope="row" class="infobox-label">Type</th><td class="infobox-data"><a href="/wiki/Astronomy" title="Astronomy">Astronomy</a>, <a href="/wiki/Mathematics" title="Mathematics">Mathematics</a>, <a href="/wiki/Science" title="Science">Science</a></td></tr><tr><th scope="row" class="infobox-label">Founder</th><td class="infobox-data"><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava of Sangamagrama</a></td></tr></tbody></table> <p>The <b>Kerala school of astronomy and mathematics</b> or the <b>Kerala school</b> was a school of <a href="/wiki/Indian_mathematics" title="Indian mathematics">mathematics</a> and <a href="/wiki/Indian_astronomy" title="Indian astronomy">astronomy</a> founded by <a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava of Sangamagrama</a> in <a href="/wiki/Kingdom_of_Tanur" title="Kingdom of Tanur">Tirur</a>, <a href="/wiki/Malappuram_district" title="Malappuram district">Malappuram</a>, <a href="/wiki/Kerala" title="Kerala">Kerala</a>, India, which included among its members: <a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a>, <a href="/wiki/Neelakanta_Somayaji" class="mw-redirect" title="Neelakanta Somayaji">Neelakanta Somayaji</a>, <a href="/wiki/Jyeshtadeva" class="mw-redirect" title="Jyeshtadeva">Jyeshtadeva</a>, <a href="/wiki/Achyuta_Pisharati" class="mw-redirect" title="Achyuta Pisharati">Achyuta Pisharati</a>, <a href="/wiki/Melpathur_Narayana_Bhattathiri" title="Melpathur Narayana Bhattathiri">Melpathur Narayana Bhattathiri</a> and <a href="/wiki/Achyuta_Panikkar" class="mw-redirect" title="Achyuta Panikkar">Achyuta Panikkar</a>. The school flourished between the 14th and 16th centuries and its original discoveries seem to have ended with <a href="/wiki/Melpathur_Narayana_Bhattathiri" title="Melpathur Narayana Bhattathiri">Narayana Bhattathiri</a> (1559–1632). In attempting to solve astronomical problems, the Kerala school independently discovered a number of important mathematical concepts. Their most important results—series expansion for trigonometric functions—were described in <a href="/wiki/Sanskrit" title="Sanskrit">Sanskrit</a> verse in a book by Neelakanta called <i><a href="/wiki/Tantrasangraha" class="mw-redirect" title="Tantrasangraha">Tantrasangraha</a></i> (around 1500), and again in a commentary on this work, called <i>Tantrasangraha-vakhya</i>, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work <i><a href="/wiki/Yuktibhasa" class="mw-redirect" title="Yuktibhasa">Yuktibhasa</a></i> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1530</span>), written in <a href="/wiki/Malayalam" title="Malayalam">Malayalam</a>, by Jyesthadeva, and also in a commentary on <i>Tantrasangraha</i>.<sup id="cite_ref-roy_1-0" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Their work, completed two centuries before the invention of <a href="/wiki/Calculus" title="Calculus">calculus</a> in Europe, provided what is now considered the first example of a <a href="/wiki/Power_series" title="Power series">power series</a> (apart from <a href="/wiki/Geometric_series" title="Geometric series">geometric series</a>).<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Background">Background</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=1" title="Edit section: Background"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Islamic scholars</a> nearly developed a general <a href="/wiki/Formula" title="Formula">formula</a> for finding <a href="/wiki/Integral" title="Integral">integrals</a> of <a href="/wiki/Polynomial" title="Polynomial">polynomials</a> by 1000 AD —and evidently could find such a formula for any polynomial in which they were interested. But, it appears, they were not interested in any polynomial of degree higher than four, at least in any of the material that has been found to date. <a href="/wiki/List_of_Indian_mathematicians" title="List of Indian mathematicians">Indian scholars</a>, on the other hand, were by the year 1600 able to use formula similar to <a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Ibn al-Haytham</a>'s sum formula for arbitrary integral powers in calculating power series for the functions in which they were interested. By the same time, they also knew how to calculate the differentials of these functions. So some of the basic ideas of calculus were known in Egypt and <a href="/wiki/Indian_mathematics" title="Indian mathematics">India</a> many centuries before <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a>. It does not appear, however, that either Islamic or Indian mathematicians saw the necessity of connecting some of the disparate ideas that we include under the name calculus. They were apparently only interested in specific cases in which these ideas were needed.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Contributions">Contributions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=2" title="Edit section: Contributions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Pages_from_Yuktibhasa.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pages_from_Yuktibhasa.jpg/420px-Pages_from_Yuktibhasa.jpg" decoding="async" width="420" height="136" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pages_from_Yuktibhasa.jpg/630px-Pages_from_Yuktibhasa.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bc/Pages_from_Yuktibhasa.jpg/840px-Pages_from_Yuktibhasa.jpg 2x" data-file-width="3750" data-file-height="1214" /></a><figcaption>Pages from the <a href="/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81" title="Yuktibhāṣā">Yuktibhasa</a> c.1530</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Infinite_series_and_calculus">Infinite series and calculus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=3" title="Edit section: Infinite series and calculus"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Kerala school has made a number of contributions to the fields of <a href="/wiki/Series_(mathematics)" title="Series (mathematics)">infinite series</a> and <a href="/wiki/Calculus" title="Calculus">calculus</a>. These include the following infinite geometric series: </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+x^{3}+\cdots {\text{ for }}|x|<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>−</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mi>x</mi> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> for </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+x^{3}+\cdots {\text{ for }}|x|<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e68546eb9286b416d3f9960da07c2393d19b0d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:41.831ex; height:5.343ex;" alt="{\displaystyle {\frac {1}{1-x}}=1+x+x^{2}+x^{3}+\cdots {\text{ for }}|x|<1}"></span><sup id="cite_ref-singh_7-0" class="reference"><a href="#cite_note-singh-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></div> <p>The Kerala school made intuitive use of <a href="/wiki/Mathematical_induction" title="Mathematical induction">mathematical induction</a>, though the <a href="/wiki/Inductive_hypothesis#Description" class="mw-redirect" title="Inductive hypothesis">inductive hypothesis</a> was not yet formulated or employed in proofs.<sup id="cite_ref-roy_1-1" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> They used this to discover a semi-rigorous proof of the result: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1^{p}+2^{p}+\cdots +n^{p}\approx {\frac {n^{p+1}}{p+1}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo>≈</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mrow> <mi>p</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1^{p}+2^{p}+\cdots +n^{p}\approx {\frac {n^{p+1}}{p+1}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54eca5f4e177d583418540fc66581d0421b0a33d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.248ex; height:6.176ex;" alt="{\displaystyle 1^{p}+2^{p}+\cdots +n^{p}\approx {\frac {n^{p+1}}{p+1}}}"></span></div> <p>for large <i>n</i>. </p><p>They applied ideas from (what was to become) <a href="/wiki/Derivative" title="Derivative">differential</a> and <a href="/wiki/Integral" title="Integral">integral</a> <a href="/wiki/Calculus" title="Calculus">calculus</a> to obtain (<a href="/wiki/Taylor_series" title="Taylor series">Taylor–Maclaurin</a>) infinite series for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09b4b55580d6a821a07ad9fe35be88976917b10b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.572ex; height:2.176ex;" alt="{\displaystyle \sin x}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/184ba70c3a71df25a25c09f34cd7f8175a9b5280" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.828ex; height:1.676ex;" alt="{\displaystyle \cos x}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \arctan x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arctan</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \arctan x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea7315ab90c047f16ec0972c15e14988ed737c1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.183ex; height:2.009ex;" alt="{\displaystyle \arctan x}"></span>.<sup id="cite_ref-bressoud_8-0" class="reference"><a href="#cite_note-bressoud-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> The <i>Tantrasangraha-vakhya</i> gives the series in verse, which when translated to mathematical notation, can be written as:<sup id="cite_ref-roy_1-2" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\arctan \left({\frac {y}{x}}\right)={\frac {1}{1}}\cdot {\frac {ry}{x}}-{\frac {1}{3}}\cdot {\frac {ry^{3}}{x^{3}}}+{\frac {1}{5}}\cdot {\frac {ry^{5}}{x^{5}}}-\cdots ,{\text{ where }}{\frac {y}{x}}\leq 1.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mi>arctan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mi>x</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>1</mn> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <mi>y</mi> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </mrow> <mo>−</mo> <mo>⋯</mo> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext> where </mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>y</mi> <mi>x</mi> </mfrac> </mrow> <mo>≤</mo> <mn>1.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\arctan \left({\frac {y}{x}}\right)={\frac {1}{1}}\cdot {\frac {ry}{x}}-{\frac {1}{3}}\cdot {\frac {ry^{3}}{x^{3}}}+{\frac {1}{5}}\cdot {\frac {ry^{5}}{x^{5}}}-\cdots ,{\text{ where }}{\frac {y}{x}}\leq 1.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f9e679d0a3927bc908069d9e83b751e6f7f292c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:65.061ex; height:6.009ex;" alt="{\displaystyle r\arctan \left({\frac {y}{x}}\right)={\frac {1}{1}}\cdot {\frac {ry}{x}}-{\frac {1}{3}}\cdot {\frac {ry^{3}}{x^{3}}}+{\frac {1}{5}}\cdot {\frac {ry^{5}}{x^{5}}}-\cdots ,{\text{ where }}{\frac {y}{x}}\leq 1.}"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\sin {\frac {x}{r}}=x-x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}+x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}+4)r^{2}}}-\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>r</mi> </mfrac> </mrow> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mi>x</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>x</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\sin {\frac {x}{r}}=x-x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}+x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}+4)r^{2}}}-\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/002464ac161b3ffc926fcc4cfe80947fde71ca5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:63.117ex; height:6.676ex;" alt="{\displaystyle r\sin {\frac {x}{r}}=x-x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}+x\cdot {\frac {x^{2}}{(2^{2}+2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}+4)r^{2}}}-\cdots }"></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r\left(1-\cos {\frac {x}{r}}\right)=r{\frac {x^{2}}{(2^{2}-2)r^{2}}}-r{\frac {x^{2}}{(2^{2}-2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}-4)r^{2}}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>r</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mn>4</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>4</mn> <mo stretchy="false">)</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r\left(1-\cos {\frac {x}{r}}\right)=r{\frac {x^{2}}{(2^{2}-2)r^{2}}}-r{\frac {x^{2}}{(2^{2}-2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}-4)r^{2}}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/141f8c5ca5292817ad24099d929940d421e24065" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:62.061ex; height:6.676ex;" alt="{\displaystyle r\left(1-\cos {\frac {x}{r}}\right)=r{\frac {x^{2}}{(2^{2}-2)r^{2}}}-r{\frac {x^{2}}{(2^{2}-2)r^{2}}}\cdot {\frac {x^{2}}{(4^{2}-4)r^{2}}}+\cdots }"></span></div> <p>where, for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=1,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=1,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c48a10fe3b7a307a26f0553f73264b775a0284c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.956ex; height:2.509ex;" alt="{\displaystyle r=1,}"></span> the series reduce to the standard power series for these trigonometric functions, for example: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <mrow> <mn>5</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <mn>7</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15a9027c77b90e40215c01281b39d37730e7e537" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.746ex; height:5.843ex;" alt="{\displaystyle \sin x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots }"></span> and</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow> <mn>4</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msup> <mrow> <mn>6</mn> <mo>!</mo> </mrow> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09ec2d1dd64d61a18f031ed242dd310840bcbbc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:32.834ex; height:5.843ex;" alt="{\displaystyle \cos x=1-{\frac {x^{2}}{2!}}+{\frac {x^{4}}{4!}}-{\frac {x^{6}}{6!}}+\cdots }"></span></div> <p>(The Kerala school did not use the "factorial" symbolism.) </p><p>The Kerala school made use of the rectification (computation of length) of the arc of a circle to give a proof of these results. (The later method of Leibniz, using quadrature (<i>i.e.</i> computation of area under the arc of the circle), was not yet developed.)<sup id="cite_ref-roy_1-3" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> They also made use of the series expansion of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \arctan x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>arctan</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \arctan x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea7315ab90c047f16ec0972c15e14988ed737c1f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.183ex; height:2.009ex;" alt="{\displaystyle \arctan x}"></span> to obtain an infinite series expression (later known as Gregory series) for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>:<sup id="cite_ref-roy_1-4" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>7</mn> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00ac5f27203f1869a2c740c98202f11a0e78e30a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.51ex; height:5.343ex;" alt="{\displaystyle {\frac {\pi }{4}}=1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}+\cdots }"></span></div> <p>Their rational approximation of the <i>error</i> for the finite sum of their series are of particular interest. For example, the error, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{i}(n+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{i}(n+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b0c8921836dbb46968f58a4ccb43b50bfb7b38e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.146ex; height:2.843ex;" alt="{\displaystyle f_{i}(n+1)}"></span>, (for <i>n</i> odd, and <i>i = 1, 2, 3</i>) for the series: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{4}}\approx 1-{\frac {1}{3}}+{\frac {1}{5}}-\cdots (-1)^{(n-1)/2}{\frac {1}{n}}+(-1)^{(n+1)/2}f_{i}(n+1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> <mo>≈</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>5</mn> </mfrac> </mrow> <mo>−</mo> <mo>⋯</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msup> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}\approx 1-{\frac {1}{3}}+{\frac {1}{5}}-\cdots (-1)^{(n-1)/2}{\frac {1}{n}}+(-1)^{(n+1)/2}f_{i}(n+1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cd4dd65ba53062fdbb233f31afca890b7615a95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:58.319ex; height:5.176ex;" alt="{\displaystyle {\frac {\pi }{4}}\approx 1-{\frac {1}{3}}+{\frac {1}{5}}-\cdots (-1)^{(n-1)/2}{\frac {1}{n}}+(-1)^{(n+1)/2}f_{i}(n+1)}"></span> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent">where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{1}(n)={\frac {1}{2n}},\ f_{2}(n)={\frac {n/2}{n^{2}+1}},\ f_{3}(n)={\frac {(n/2)^{2}+1}{(n^{2}+5)n/2}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>,</mo> <mtext> </mtext> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </mrow> <mrow> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>5</mn> <mo stretchy="false">)</mo> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{1}(n)={\frac {1}{2n}},\ f_{2}(n)={\frac {n/2}{n^{2}+1}},\ f_{3}(n)={\frac {(n/2)^{2}+1}{(n^{2}+5)n/2}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edb6f626103c3c7e3b9610041793ad5fe85aa540" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:52.862ex; height:6.676ex;" alt="{\displaystyle f_{1}(n)={\frac {1}{2n}},\ f_{2}(n)={\frac {n/2}{n^{2}+1}},\ f_{3}(n)={\frac {(n/2)^{2}+1}{(n^{2}+5)n/2}}.}"></span></div></div> <p>They manipulated the terms, using the partial fraction expansion of :<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{n^{3}-n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mi>n</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{n^{3}-n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/236cb0b2a9e913d901bef3f5c215005ce4485ddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:7.52ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{n^{3}-n}}}"></span> to obtain a more rapidly converging series for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span>:<sup id="cite_ref-roy_1-5" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996643573"><div class="block-indent"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\pi }{4}}={\frac {3}{4}}+{\frac {1}{3^{3}-3}}-{\frac {1}{5^{3}-5}}+{\frac {1}{7^{3}-7}}-\cdots }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>4</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>5</mn> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msup> <mn>7</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>7</mn> </mrow> </mfrac> </mrow> <mo>−</mo> <mo>⋯</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\pi }{4}}={\frac {3}{4}}+{\frac {1}{3^{3}-3}}-{\frac {1}{5^{3}-5}}+{\frac {1}{7^{3}-7}}-\cdots }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a8ef8b29347050c41378497b9957830d2c09f620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:42.517ex; height:5.843ex;" alt="{\displaystyle {\frac {\pi }{4}}={\frac {3}{4}}+{\frac {1}{3^{3}-3}}-{\frac {1}{5^{3}-5}}+{\frac {1}{7^{3}-7}}-\cdots }"></span></div> <p>They used the improved series to derive a rational expression,<sup id="cite_ref-roy_1-6" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 104348/33215}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>104348</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>33215</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 104348/33215}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba01914e1a7cddcb3e87a95db9a383bee60134f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.949ex; height:2.843ex;" alt="{\displaystyle 104348/33215}"></span> for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> correct up to nine decimal places, i.e. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3.141592653}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3.141592653</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3.141592653}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78b03e4a30e2d4b6e087e3d1491912edb689394f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.271ex; height:2.176ex;" alt="{\displaystyle 3.141592653}"></span>. They made use of an intuitive notion of a <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a> to compute these results.<sup id="cite_ref-roy_1-7" class="reference"><a href="#cite_note-roy-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The Kerala school mathematicians also gave a semi-rigorous method of differentiation of some trigonometric functions,<sup id="cite_ref-katz_9-0" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> though the notion of a function, or of exponential or logarithmic functions, was not yet formulated. </p> <div class="mw-heading mw-heading3"><h3 id="Recognition">Recognition</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=4" title="Edit section: Recognition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1825 John Warren published a memoir on the division of time in southern India,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> called the <i>Kala Sankalita</i>, which briefly mentions the discovery of infinite series by Kerala astronomers. </p><p>The works of the Kerala school were first written up for the Western world by Englishman <a href="/wiki/C._M._Whish" title="C. M. Whish">C. M. Whish</a> in 1835. According to Whish, the Kerala mathematicians had "laid the foundation for a complete system of fluxions" and these works abounded "with fluxional forms and series to be found in no work of foreign countries".<sup id="cite_ref-whish_11-0" class="reference"><a href="#cite_note-whish-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> However, Whish's results were almost completely neglected until over a century later, when the discoveries of the Kerala school were investigated again by <a href="/wiki/C._T._Rajagopal" class="mw-redirect" title="C. T. Rajagopal">C. T. Rajagopal</a> and his associates. Their work includes commentaries on the proofs of the arctan series in <i>Yuktibhasa</i> given in two papers,<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> a commentary on the <i>Yuktibhasa</i><span class="nowrap" style="padding-left:0.1em;">'</span>s proof of the sine and cosine series<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> and two papers that provide the <a href="/wiki/Sanskrit" title="Sanskrit">Sanskrit</a> verses of the <i>Tantrasangrahavakhya</i> for the series for arctan, sin, and cosine (with English translation and commentary).<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p><p>In 1972 <a href="/wiki/K._V._Sarma" title="K. V. Sarma">K. V. Sarma</a> published his <i><a href="/wiki/A_History_of_the_Kerala_School_of_Hindu_Astronomy" title="A History of the Kerala School of Hindu Astronomy">A History of the Kerala School of Hindu Astronomy</a></i> which described features of the School such as the continuity of knowledge transmission from the 13th to the 17th century: <a href="/wiki/Govinda_Bhattathiri" title="Govinda Bhattathiri">Govinda Bhattathiri</a> to <a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a> to <a href="/wiki/Damodara" title="Damodara">Damodara</a> to <a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nilakantha Somayaji</a> to <a href="/wiki/Jyesthadeva" class="mw-redirect" title="Jyesthadeva">Jyesthadeva</a> to <a href="/wiki/Acyuta_Pisarati" class="mw-redirect" title="Acyuta Pisarati">Acyuta Pisarati</a>. Transmission from teacher to pupil conserved knowledge in "a practical, demonstrative discipline like astronomy at a time when there was not a proliferation of printed books and public schools." </p><p>In 1994 it was argued that the <a href="/wiki/Heliocentric_model" class="mw-redirect" title="Heliocentric model">heliocentric model</a> had been adopted about 1500 A.D. in Kerala.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Possible_transmission_of_Kerala_school_results_to_Europe">Possible transmission of Kerala school results to Europe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=5" title="Edit section: Possible transmission of Kerala school results to Europe"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A. K. Bag suggested in 1979 that knowledge of these results might have been transmitted to Europe through the trade route from <a href="/wiki/Kerala" title="Kerala">Kerala</a> by traders and <a href="/wiki/Jesuit" class="mw-redirect" title="Jesuit">Jesuit</a> missionaries.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Kerala was in continuous contact with China and <a href="/wiki/Arabia" class="mw-redirect" title="Arabia">Arabia</a>, and <a href="/wiki/Europe" title="Europe">Europe</a>. The suggestion of some communication routes and a chronology by some scholars<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-almeida_20-0" class="reference"><a href="#cite_note-almeida-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> could make such a transmission a possibility; however, there is no direct evidence by way of relevant manuscripts that such a transmission took place.<sup id="cite_ref-almeida_20-1" class="reference"><a href="#cite_note-almeida-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> According to <a href="/wiki/David_Bressoud" title="David Bressoud">David Bressoud</a>, "there is no evidence that the Indian work of series was known beyond India, or even outside of Kerala, until the nineteenth century".<sup id="cite_ref-bressoud_8-1" class="reference"><a href="#cite_note-bressoud-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-gold_21-0" class="reference"><a href="#cite_note-gold-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> V. J. Katz notes some of the ideas of the Kerala school have similarities to the work of 11th-century Iraqi scholar <a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Ibn al-Haytham</a>,<sup id="cite_ref-katz_9-1" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> suggesting a possible transmission of ideas from <a href="/wiki/Islamic_mathematics" class="mw-redirect" title="Islamic mathematics">Islamic mathematics</a> to Kerala.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </p><p>Both Indian and <a href="/wiki/Islamic_mathematics" class="mw-redirect" title="Islamic mathematics">Arab</a> scholars made discoveries before the 17th century that are now considered a part of calculus.<sup id="cite_ref-katz_9-2" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> According to Katz, they were yet to "combine many differing ideas under the two unifying themes of the <a href="/wiki/Derivative" title="Derivative">derivative</a> and the <a href="/wiki/Integral" title="Integral">integral</a>, show the connection between the two, and turn calculus into the great problem-solving tool we have today", like <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> and <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Leibniz</a>.<sup id="cite_ref-katz_9-3" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The intellectual careers of both Newton and Leibniz are well documented and there is no indication of their work not being their own;<sup id="cite_ref-katz_9-4" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> however, it is not known with certainty whether the immediate <i>predecessors</i> of Newton and Leibniz, "including, in particular, <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Fermat</a> and Roberval, learned of some of the ideas of the Islamic and Indian mathematicians through sources of which we are not now aware".<sup id="cite_ref-katz_9-5" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> This is an active area of current research, especially in the manuscript collections of Spain and <a href="/wiki/Maghreb" title="Maghreb">Maghreb</a>, research that is now being pursued, among other places, at the <span title="French-language text"><span lang="fr" style="font-style: normal;"><a href="/wiki/Centre_national_de_la_recherche_scientifique" class="mw-redirect" title="Centre national de la recherche scientifique">Centre national de la recherche scientifique</a></span></span> in <a href="/wiki/Paris" title="Paris">Paris</a>.<sup id="cite_ref-katz_9-6" class="reference"><a href="#cite_note-katz-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=6" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Indian_astronomy" title="Indian astronomy">Indian astronomy</a></li> <li><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a></li> <li><a href="/wiki/Indian_mathematicians" class="mw-redirect" title="Indian mathematicians">Indian mathematicians</a></li> <li><a href="/wiki/History_of_mathematics" title="History of mathematics">History of mathematics</a></li> <li><a href="/wiki/A_History_of_the_Kerala_School_of_Hindu_Astronomy" title="A History of the Kerala School of Hindu Astronomy">A History of the Kerala School of Hindu Astronomy</a></li> <li><a href="/wiki/List_of_astronomers_and_mathematicians_of_the_Kerala_school" title="List of astronomers and mathematicians of the Kerala school">List of astronomers and mathematicians of the Kerala school</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=7" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-roy-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-roy_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-roy_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-roy_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-roy_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-roy_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-roy_1-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-roy_1-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-roy_1-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text">Roy, Ranjan. 1990. "Discovery of the Series Formula for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> by Leibniz, Gregory, and Nilakantha." <i>Mathematics Magazine</i> (Mathematical Association of America) 63(5):291–306.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">(<a href="#CITEREFStillwell2004">Stillwell 2004</a>, p. 173)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">(<a href="#CITEREFBressoud2002">Bressoud 2002</a>, p. 12) Quote: "There is no evidence that the Indian work on series was known beyond India, or even outside Kerala, until the nineteenth century. Gold and Pingree assert [4] that by the time these series were rediscovered in Europe, they had, for all practical purposes, been lost to India. The expansions of the sine, cosine, and arc tangent had been passed down through several generations of disciples, but they remained sterile observations for which no one could find much use."</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="#CITEREFPlofker2001">Plofker 2001</a>, p. 293 Quote: "It is not unusual to encounter in discussions of Indian mathematics such assertions as that "the concept of differentiation was understood [in India] from the time of Manjula (... in the 10th century)" [Joseph 1991, 300], or that "we may consider Madhava to have been the founder of mathematical analysis" (Joseph 1991, 293), or that Bhaskara II may claim to be "the precursor of Newton and Leibniz in the discovery of the principle of the differential calculus" (Bag 1979, 294). ... The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world (e.g., in (Bag 1979, 285)). ... It should be borne in mind, however, that such an emphasis on the similarity of Sanskrit (or Malayalam) and Latin mathematics risks diminishing our ability fully to see and comprehend the former. To speak of the Indian "discovery of the principle of the differential calculus" somewhat obscures the fact that Indian techniques for expressing changes in the Sine by means of the Cosine or vice versa, as in the examples we have seen, remained within that specific trigonometric context. The differential "principle" was not generalized to arbitrary functions—in fact, the explicit notion of an arbitrary function, not to mention that of its derivative or an algorithm for taking the derivative, is irrelevant here"</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="#CITEREFPingree1992">Pingree 1992</a>, p. 562 Quote: "One example I can give you relates to the Indian Mādhava's demonstration, in about 1400 A.D., of the infinite power series of trigonometrical functions using geometrical and algebraic arguments. When this was first described in English by Charles Whish, in the 1830s, it was heralded as the Indians' discovery of the calculus. This claim and Mādhava's achievements were ignored by Western historians, presumably at first because they could not admit that an Indian discovered the calculus, but later because no one read anymore the <i>Transactions of the Royal Asiatic Society</i>, in which Whish's article was published. The matter resurfaced in the 1950s, and now we have the Sanskrit texts properly edited, and we understand the clever way that Mādhava derived the series <i>without</i> the calculus; but many historians still find it impossible to conceive of the problem and its solution in terms of anything other than the calculus and proclaim that the calculus is what Mādhava found. In this case the elegance and brilliance of Mādhava's mathematics are being distorted as they are buried under the current mathematical solution to a problem to which he discovered an alternate and powerful solution."</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a href="#CITEREFKatz1995">Katz 1995</a>, pp. 173–174 Quote: "How close did Islamic and Indian scholars come to inventing the calculus? Islamic scholars nearly developed a general formula for finding integrals of polynomials by A.D. 1000—and evidently could find such a formula for any polynomial in which they were interested. But, it appears, they were not interested in any polynomial of degree higher than four, at least in any of the material that has come down to us. Indian scholars, on the other hand, were by 1600 able to use ibn al-Haytham's sum formula for arbitrary integral powers in calculating power series for the functions in which they were interested. By the same time, they also knew how to calculate the differentials of these functions. So some of the basic ideas of calculus were known in Egypt and India many centuries before Newton. It does not appear, however, that either Islamic or Indian mathematicians saw the necessity of connecting some of the disparate ideas that we include under the name calculus. They were apparently only interested in specific cases in which these ideas were needed.<br />    There is no danger, therefore, that we will have to rewrite the history texts to remove the statement that Newton and Leibniz invented the calculus. They were certainly the ones who were able to combine many differing ideas under the two unifying themes of the derivative and the integral, show the connection between them, and turn the calculus into the great problem-solving tool we have today."</span> </li> <li id="cite_note-singh-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-singh_7-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSingh1936" class="citation journal cs1">Singh, A. N. (1936). "On the Use of Series in Hindu Mathematics". <i>Osiris</i>. <b>1</b>: 606–628. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F368443">10.1086/368443</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144760421">144760421</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Osiris&rft.atitle=On+the+Use+of+Series+in+Hindu+Mathematics&rft.volume=1&rft.pages=606-628&rft.date=1936&rft_id=info%3Adoi%2F10.1086%2F368443&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144760421%23id-name%3DS2CID&rft.aulast=Singh&rft.aufirst=A.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-bressoud-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-bressoud_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bressoud_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Bressoud, David. 2002. "Was Calculus Invented in India?" <i>The College Mathematics Journal</i> (Mathematical Association of America). 33(1):2–13.</span> </li> <li id="cite_note-katz-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-katz_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-katz_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-katz_9-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-katz_9-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-katz_9-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-katz_9-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-katz_9-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text">Katz, V. J. 1995. "Ideas of Calculus in Islam and India." (<a rel="nofollow" class="external text" href="https://maa.org/sites/default/files/0025570x37767.di021190.02p0147a.pdf">pdf</a>) <i>Mathematics Magazine</i> (Mathematical Association of America), 68(3):163-174.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">John Warren (1825) <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nttCAAAAcAAJ">A Collection of Memoirs on Various Modes According to which Nations of the Southern Part of India Divide Time</a> from <a href="/wiki/Google_Books" title="Google Books">Google Books</a></span> </li> <li id="cite_note-whish-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-whish_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWhish1835" class="citation journal cs1">Whish, Charles M. (1835). <a rel="nofollow" class="external text" href="https://archive.org/details/transactionsofro03asia/page/509/">"XXXIII. On the Hindú Quadrature of the Circle, and the infinite Series of the proportion of the circumference to the diameter exhibited in the four S'ástras, the Tantra Sangraham, the Yucti Bháshá, Carana Padhati, and Sadratnamáka"</a>. <i>Transactions of the Royal Asiatic Society</i>. <b>3</b>: 509–523.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Royal+Asiatic+Society&rft.atitle=XXXIII.+On+the+Hind%C3%BA+Quadrature+of+the+Circle%2C+and+the+infinite+Series+of+the+proportion+of+the+circumference+to+the+diameter+exhibited+in+the+four+S%27%C3%A1stras%2C+the+Tantra+Sangraham%2C+the+Yucti+Bh%C3%A1sh%C3%A1%2C+Carana+Padhati%2C+and+Sadratnam%C3%A1ka&rft.volume=3&rft.pages=509-523&rft.date=1835&rft.aulast=Whish&rft.aufirst=Charles+M.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Ftransactionsofro03asia%2Fpage%2F509%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRajagopalRangachari1949" class="citation journal cs1">Rajagopal, C.; Rangachari, M. S. (1949). "A Neglected Chapter of Hindu Mathematics". <i>Scripta Mathematica</i>. <b>15</b>: 201–209.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scripta+Mathematica&rft.atitle=A+Neglected+Chapter+of+Hindu+Mathematics&rft.volume=15&rft.pages=201-209&rft.date=1949&rft.aulast=Rajagopal&rft.aufirst=C.&rft.au=Rangachari%2C+M.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRajagopalRangachari1951" class="citation journal cs1">Rajagopal, C.; Rangachari, M. S. (1951). "On the Hindu proof of Gregory's series". <i>Scripta Mathematica</i>. <b>17</b>: 65–74.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scripta+Mathematica&rft.atitle=On+the+Hindu+proof+of+Gregory%27s+series&rft.volume=17&rft.pages=65-74&rft.date=1951&rft.aulast=Rajagopal&rft.aufirst=C.&rft.au=Rangachari%2C+M.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRajagopalVenkataraman1949" class="citation journal cs1">Rajagopal, C.; Venkataraman, A. (1949). "The sine and cosine power series in Hindu mathematics". <i>Journal of the Royal Asiatic Society of Bengal (Science)</i>. <b>15</b>: 1–13.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+Royal+Asiatic+Society+of+Bengal+%28Science%29&rft.atitle=The+sine+and+cosine+power+series+in+Hindu+mathematics&rft.volume=15&rft.pages=1-13&rft.date=1949&rft.aulast=Rajagopal&rft.aufirst=C.&rft.au=Venkataraman%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRajagopalRangachari1977" class="citation journal cs1">Rajagopal, C.; Rangachari, M. S. (1977). "On an untapped source of medieval Keralese mathematics". <i>Archive for History of Exact Sciences</i>. <b>18</b> (2): 89–102. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00348142">10.1007/BF00348142</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51861422">51861422</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=On+an+untapped+source+of+medieval+Keralese+mathematics&rft.volume=18&rft.issue=2&rft.pages=89-102&rft.date=1977&rft_id=info%3Adoi%2F10.1007%2FBF00348142&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A51861422%23id-name%3DS2CID&rft.aulast=Rajagopal&rft.aufirst=C.&rft.au=Rangachari%2C+M.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRajagopalRangachari1986" class="citation journal cs1">Rajagopal, C.; Rangachari, M. S. (1986). "On Medieval Kerala Mathematics". <i>Archive for History of Exact Sciences</i>. <b>35</b> (2): 91–99. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF00357622">10.1007/BF00357622</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:121678430">121678430</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Archive+for+History+of+Exact+Sciences&rft.atitle=On+Medieval+Kerala+Mathematics&rft.volume=35&rft.issue=2&rft.pages=91-99&rft.date=1986&rft_id=info%3Adoi%2F10.1007%2FBF00357622&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A121678430%23id-name%3DS2CID&rft.aulast=Rajagopal&rft.aufirst=C.&rft.au=Rangachari%2C+M.+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">K. Ramasubramanian, M. D. Srinivas & M. S. Sriram (1994) <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101223145939/http://www.physics.iitm.ac.in/~labs/amp/kerala-astronomy.pdf">Modification of the earlier Indian planetary theory by the Kerala astronomers (c. 1500 A.D.) and the implied heliocentric picture of planetary motion</a>, <i><a href="/wiki/Current_Science" title="Current Science">Current Science</a></i> <a rel="nofollow" class="external text" href="https://www.currentscience.ac.in/show.issue.php?volume=66&issue=10"><b>66</b> (10)</a>: 784–90</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">A. K. Bag (1979) <i>Mathematics in ancient and medieval India</i>. Varanasi/Delhi: Chaukhambha Orientalia. page 285.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRaju2001" class="citation journal cs1"><a href="/wiki/C._K._Raju" title="C. K. Raju">Raju, C. K.</a> (2001). "Computers, Mathematics Education, and the Alternative Epistemology of the Calculus in the Yuktibhasa". <i>Philosophy East and West</i>. <b>51</b> (3): 325–362. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1353%2Fpew.2001.0045">10.1353/pew.2001.0045</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170341845">170341845</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophy+East+and+West&rft.atitle=Computers%2C+Mathematics+Education%2C+and+the+Alternative+Epistemology+of+the+Calculus+in+the+Yuktibhasa&rft.volume=51&rft.issue=3&rft.pages=325-362&rft.date=2001&rft_id=info%3Adoi%2F10.1353%2Fpew.2001.0045&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170341845%23id-name%3DS2CID&rft.aulast=Raju&rft.aufirst=C.+K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-almeida-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-almeida_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-almeida_20-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlmeidaJohnZadorozhnyy2001" class="citation journal cs1">Almeida, D. F.; John, J. K.; Zadorozhnyy, A. (2001). "Keralese Mathematics: Its Possible Transmission to Europe and the Consequential Educational Implications". <i>Journal of Natural Geometry</i>. <b>20</b>: 77–104.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Natural+Geometry&rft.atitle=Keralese+Mathematics%3A+Its+Possible+Transmission+to+Europe+and+the+Consequential+Educational+Implications&rft.volume=20&rft.pages=77-104&rft.date=2001&rft.aulast=Almeida&rft.aufirst=D.+F.&rft.au=John%2C+J.+K.&rft.au=Zadorozhnyy%2C+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-gold-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-gold_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoldPingree1991" class="citation journal cs1">Gold, D.; Pingree, D. (1991). "A hitherto unknown Sanskrit work concerning Madhava's derivation of the power series for sine and cosine". <i>Historia Scientiarum</i>. <b>42</b>: 49–65.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Scientiarum&rft.atitle=A+hitherto+unknown+Sanskrit+work+concerning+Madhava%27s+derivation+of+the+power+series+for+sine+and+cosine&rft.volume=42&rft.pages=49-65&rft.date=1991&rft.aulast=Gold&rft.aufirst=D.&rft.au=Pingree%2C+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><a href="#CITEREFKatz1995">Katz 1995</a>, p. 174.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBressoud2002" class="citation cs2">Bressoud, David (2002), "Was Calculus Invented in India?", <i>The College Mathematics Journal</i>, <b>33</b> (1): 2–13, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1558972">10.2307/1558972</a>, <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1558972">1558972</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+College+Mathematics+Journal&rft.atitle=Was+Calculus+Invented+in+India%3F&rft.volume=33&rft.issue=1&rft.pages=2-13&rft.date=2002&rft_id=info%3Adoi%2F10.2307%2F1558972&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1558972%23id-name%3DJSTOR&rft.aulast=Bressoud&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><a href="/wiki/R.C_Gupta" class="mw-redirect" title="R.C Gupta">Gupta, R. C.</a> (1969) "Second Order of Interpolation of Indian Mathematics", <i>Indian Journal of History of Science</i> 4: 92-94</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHayashi2003" class="citation cs2 cs1-prop-long-vol">Hayashi, Takao (2003), "Indian Mathematics", in Grattan-Guinness, Ivor (ed.), <i>Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences</i>, vol. 1, pp. 118–130, Baltimore, MD: The Johns Hopkins University Press, 976 pages, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8018-7396-7" title="Special:BookSources/0-8018-7396-7"><bdi>0-8018-7396-7</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Indian+Mathematics&rft.btitle=Companion+Encyclopedia+of+the+History+and+Philosophy+of+the+Mathematical+Sciences&rft.place=Baltimore%2C+MD&rft.pub=The+Johns+Hopkins+University+Press%2C+976+pages&rft.date=2003&rft.isbn=0-8018-7396-7&rft.aulast=Hayashi&rft.aufirst=Takao&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoseph2000" class="citation cs2">Joseph, G. G. (2000), <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/crestofpeacockno00jose"><i>The Crest of the Peacock: The Non-European Roots of Mathematics</i></a></span>, Princeton, NJ: <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-00659-8" title="Special:BookSources/0-691-00659-8"><bdi>0-691-00659-8</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Crest+of+the+Peacock%3A+The+Non-European+Roots+of+Mathematics&rft.place=Princeton%2C+NJ&rft.pub=Princeton+University+Press&rft.date=2000&rft.isbn=0-691-00659-8&rft.aulast=Joseph&rft.aufirst=G.+G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fcrestofpeacockno00jose&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatz1995" class="citation cs2">Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", <i>Mathematics Magazine</i>, <b>68</b> (3): 163–174, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2691411">10.2307/2691411</a>, <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2691411">2691411</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Magazine&rft.atitle=Ideas+of+Calculus+in+Islam+and+India&rft.volume=68&rft.issue=3&rft.pages=163-174&rft.date=1995&rft_id=info%3Adoi%2F10.2307%2F2691411&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2691411%23id-name%3DJSTOR&rft.aulast=Katz&rft.aufirst=Victor+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li>Parameswaran, S. (1992) "Whish's showroom revisited", <a href="/wiki/Mathematical_Gazette" class="mw-redirect" title="Mathematical Gazette">Mathematical Gazette</a> 76, no. 475 pages 28–36</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPingree1992" class="citation cs2"><a href="/wiki/David_Pingree" title="David Pingree">Pingree, David</a> (1992), "Hellenophilia versus the History of Science", <i>Isis</i>, <b>83</b> (4): 554–563, <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1992Isis...83..554P">1992Isis...83..554P</a>, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F356288">10.1086/356288</a>, <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/234257">234257</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:68570164">68570164</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Hellenophilia+versus+the+History+of+Science&rft.volume=83&rft.issue=4&rft.pages=554-563&rft.date=1992&rft_id=info%3Adoi%2F10.1086%2F356288&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A68570164%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F234257%23id-name%3DJSTOR&rft_id=info%3Abibcode%2F1992Isis...83..554P&rft.aulast=Pingree&rft.aufirst=David&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlofker1996" class="citation cs2">Plofker, Kim (1996), "An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text", <i>Historia Mathematica</i>, <b>23</b> (3): 246–256, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fhmat.1996.0026">10.1006/hmat.1996.0026</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Mathematica&rft.atitle=An+Example+of+the+Secant+Method+of+Iterative+Approximation+in+a+Fifteenth-Century+Sanskrit+Text&rft.volume=23&rft.issue=3&rft.pages=246-256&rft.date=1996&rft_id=info%3Adoi%2F10.1006%2Fhmat.1996.0026&rft.aulast=Plofker&rft.aufirst=Kim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlofker2001" class="citation cs2">Plofker, Kim (2001), "The "Error" in the Indian "Taylor Series Approximation" to the Sine", <i>Historia Mathematica</i>, <b>28</b> (4): 283–295, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fhmat.2001.2331">10.1006/hmat.2001.2331</a></span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Mathematica&rft.atitle=The+%22Error%22+in+the+Indian+%22Taylor+Series+Approximation%22+to+the+Sine&rft.volume=28&rft.issue=4&rft.pages=283-295&rft.date=2001&rft_id=info%3Adoi%2F10.1006%2Fhmat.2001.2331&rft.aulast=Plofker&rft.aufirst=Kim&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlofker2007" class="citation cs2">Plofker, K. (20 July 2007), "Mathematics of India", in Katz, Victor J. (ed.), <i>The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook</i>, Princeton, NJ: Princeton University Press, 685 pages (published 2007), pp. 385–514, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11485-9" title="Special:BookSources/978-0-691-11485-9"><bdi>978-0-691-11485-9</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mathematics+of+India&rft.btitle=The+Mathematics+of+Egypt%2C+Mesopotamia%2C+China%2C+India%2C+and+Islam%3A+A+Sourcebook&rft.place=Princeton%2C+NJ&rft.pages=385-514&rft.pub=Princeton+University+Press%2C+685+pages&rft.date=2007-07-20&rft.isbn=978-0-691-11485-9&rft.aulast=Plofker&rft.aufirst=K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li>C. K. Raju. 'Computers, mathematics education, and the alternative epistemology of the calculus in the Yuktibhâsâ', <i>Philosophy East and West</i> <b>51</b>, University of Hawaii Press, 2001.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRoy1990" class="citation cs2">Roy, Ranjan (1990), "Discovery of the Series Formula for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \pi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be4ba0bb8df3af72e90a0535fabcc17431e540a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.332ex; height:1.676ex;" alt="{\displaystyle \pi }"></span> by Leibniz, Gregory, and Nilakantha", <i>Mathematics Magazine</i>, <b>63</b> (5): 291–306, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2690896">10.2307/2690896</a>, <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2690896">2690896</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Magazine&rft.atitle=Discovery+of+the+Series+Formula+for+MATH+RENDER+ERROR+by+Leibniz%2C+Gregory%2C+and+Nilakantha&rft.volume=63&rft.issue=5&rft.pages=291-306&rft.date=1990&rft_id=info%3Adoi%2F10.2307%2F2690896&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2690896%23id-name%3DJSTOR&rft.aulast=Roy&rft.aufirst=Ranjan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSarmaHariharan1991" class="citation journal cs1">Sarma, K. V.; Hariharan, S. (1991). "Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy – an analytical appraisal". <i>Indian J. Hist. Sci</i>. <b>26</b> (2): 185–207.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Indian+J.+Hist.+Sci.&rft.atitle=Yuktibhasa+of+Jyesthadeva+%3A+a+book+of+rationales+in+Indian+mathematics+and+astronomy+%E2%80%93+an+analytical+appraisal&rft.volume=26&rft.issue=2&rft.pages=185-207&rft.date=1991&rft.aulast=Sarma&rft.aufirst=K.+V.&rft.au=Hariharan%2C+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSingh1936" class="citation cs2">Singh, A. N. (1936), "On the Use of Series in Hindu Mathematics", <i>Osiris</i>, <b>1</b>: 606–628, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F368443">10.1086/368443</a>, <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/301627">301627</a>, <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144760421">144760421</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Osiris&rft.atitle=On+the+Use+of+Series+in+Hindu+Mathematics&rft.volume=1&rft.pages=606-628&rft.date=1936&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144760421%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F301627%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1086%2F368443&rft.aulast=Singh&rft.aufirst=A.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStillwell2004" class="citation cs2">Stillwell, John (2004), <i>Mathematics and its History</i> (2 ed.), Berlin and New York: Springer, 568 pages, <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-95336-1" title="Special:BookSources/0-387-95336-1"><bdi>0-387-95336-1</bdi></a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+and+its+History&rft.place=Berlin+and+New+York&rft.edition=2&rft.pub=Springer%2C+568+pages&rft.date=2004&rft.isbn=0-387-95336-1&rft.aulast=Stillwell&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AKerala+school+of+astronomy+and+mathematics" class="Z3988"></span>.</li> <li>Tacchi Venturi. 'Letter by Matteo Ricci to Petri Maffei on 1 Dec 1581', <i>Matteo Ricci S.I., Le Lettre Dalla Cina 1580–1610</i>, vol. 2, Macerata, 1613.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 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href="http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_4.html">Possible transmission of Keralese mathematics to Europe</a>, <i>MacTutor History of Mathematics archive</i>, 2002.</li> <li><a rel="nofollow" class="external text" href="http://www.physorg.com/news106238636.html">"Indians predated Newton 'discovery' by 250 years"</a> <i>phys.org,</i> 2007</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Indian_mathematics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Indian_mathematics" title="Template:Indian mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Indian_mathematics" title="Template talk:Indian mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Indian_mathematics" title="Special:EditPage/Template:Indian mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Indian_mathematics" style="font-size:114%;margin:0 4em"><a href="/wiki/Indian_mathematics" title="Indian mathematics">Indian mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_Indian_mathematicians" title="List of Indian mathematicians">Mathematicians</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Ancient</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apastamba_Dharmasutra" title="Apastamba Dharmasutra">Apastamba</a></li> <li><a href="/wiki/Baudhayana_sutras" title="Baudhayana sutras">Baudhayana</a></li> <li><a href="/wiki/K%C4%81ty%C4%81yana" title="Kātyāyana">Katyayana</a></li> <li><a href="/wiki/Manava" title="Manava">Manava</a></li> <li><a href="/wiki/P%C4%81%E1%B9%87ini" title="Pāṇini">Pāṇini</a></li> <li><a href="/wiki/Pingala" title="Pingala">Pingala</a></li> <li><a href="/wiki/Yajnavalkya" title="Yajnavalkya">Yajnavalkya</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classical</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Aryabhata" title="Aryabhata">Āryabhaṭa I</a></li> <li><a href="/wiki/Aryabhata_II" title="Aryabhata II">Āryabhaṭa II</a></li> <li><a href="/wiki/Bh%C4%81skara_I" title="Bhāskara I">Bhāskara I</a></li> <li><a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a></li> <li><a href="/wiki/Melpathur_Narayana_Bhattathiri" title="Melpathur Narayana Bhattathiri">Melpathur Narayana Bhattathiri</a></li> <li><a href="/wiki/Brahmadeva" title="Brahmadeva">Brahmadeva</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/wiki/Govindasv%C4%81mi" title="Govindasvāmi">Govindasvāmi</a></li> <li><a href="/wiki/Halayudha" title="Halayudha">Halayudha</a></li> <li><a href="/wiki/Jye%E1%B9%A3%E1%B9%ADhadeva" title="Jyeṣṭhadeva">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Kamalakara" title="Kamalakara">Kamalakara</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Mādhava of Saṅgamagrāma</a></li> <li><a href="/wiki/Mah%C4%81v%C4%ABra_(mathematician)" title="Mahāvīra (mathematician)">Mahāvīra</a></li> <li><a href="/wiki/Mahendra_S%C5%ABri" title="Mahendra Sūri">Mahendra Sūri</a></li> <li><a href="/wiki/Munishvara" title="Munishvara">Munishvara</a></li> <li><a href="/wiki/Narayana_Pandit" class="mw-redirect" title="Narayana Pandit">Narayana</a></li> <li><a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a></li> <li><a href="/wiki/Achyuta_Pisharati" class="mw-redirect" title="Achyuta Pisharati">Achyuta Pisharati</a></li> <li><a href="/wiki/Jagannatha_Samrat" title="Jagannatha Samrat">Jagannatha Samrat</a></li> <li><a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nilakantha Somayaji</a></li> <li><a href="/wiki/%C5%9Ar%C4%ABpati" title="Śrīpati">Śrīpati</a></li> <li><a href="/wiki/Sridhara" title="Sridhara">Sridhara</a></li> <li><a href="/wiki/Gangesha_Upadhyaya" class="mw-redirect" title="Gangesha Upadhyaya">Gangesha Upadhyaya</a></li> <li><a href="/wiki/Var%C4%81hamihira" title="Varāhamihira">Varāhamihira</a></li> <li><a href="/wiki/Sankara_Variar" title="Sankara Variar">Sankara Variar</a></li> <li><a href="/wiki/Virasena" title="Virasena">Virasena</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Srinivasa_Ramanujan" title="Srinivasa Ramanujan">Srinivasa Ramanujan</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Satyendra Nath Bose</a></li> <li><a href="/wiki/P.C._Mahalanobis" class="mw-redirect" title="P.C. Mahalanobis">P.C. Mahalanobis</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a></li> <li><a href="/wiki/C.R._Rao" class="mw-redirect" title="C.R. Rao">C.R. Rao</a></li> <li><a href="/wiki/Veeravalli_S._Varadarajan" title="Veeravalli S. Varadarajan">Veeravalli S. Varadarajan</a></li> <li><a href="/wiki/S._R._Srinivasa_Varadhan" title="S. R. Srinivasa Varadhan">S. R. Srinivasa Varadhan</a></li> <li><a href="/wiki/K._R._Parthasarathy_(probabilist)" title="K. R. Parthasarathy (probabilist)">K. R. Parthasarathy (probabilist)</a></li> <li><a href="/wiki/M._S._Narasimhan" title="M. S. Narasimhan">M. S. Narasimhan</a></li> <li><a href="/wiki/C._S._Seshadri" title="C. S. Seshadri">C. S. Seshadri</a></li> <li><a href="/wiki/Harish-Chandra" title="Harish-Chandra">Harish-Chandra</a></li> <li><a href="/wiki/Subbayya_Sivasankaranarayana_Pillai" title="Subbayya Sivasankaranarayana Pillai">Subbayya Sivasankaranarayana Pillai</a></li> <li><a href="/wiki/Tilak_Raj_Prabhakar" title="Tilak Raj Prabhakar">Tilak Raj Prabhakar</a></li> <li><a href="/wiki/Manjul_Bhargava" title="Manjul Bhargava">Manjul Bhargava</a></li> <li><a href="/wiki/Akshay_Venkatesh" title="Akshay Venkatesh">Akshay Venkatesh</a></li> <li><a href="/wiki/Ravi_Vakil" title="Ravi Vakil">Ravi Vakil</a></li> <li><a href="/wiki/Kannan_Soundararajan" title="Kannan Soundararajan">Kannan Soundararajan</a></li> <li><a href="/wiki/Template:SSBPST_recipients_in_Mathematical_Science" title="Template:SSBPST recipients in Mathematical Science">Shanti Swarup Bhatnagar Prize recipients in Mathematical Science</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Aryabhatiya" title="Aryabhatiya">Aryabhatiya</a></i></li> <li><a href="/wiki/Bakhshali_manuscript" title="Bakhshali manuscript">Bakhshali manuscript</a></li> <li><i><a href="/wiki/Bijaganita" title="Bijaganita">Bijaganita</a></i></li> <li><i><a href="/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta" title="Brāhmasphuṭasiddhānta">Brāhmasphuṭasiddhānta</a></i></li> <li><i><a href="/wiki/Ganita_Kaumudi" title="Ganita Kaumudi">Ganita Kaumudi</a></i></li> <li><i><a href="/wiki/Kanakkusaram" title="Kanakkusaram">Kanakkusaram</a></i></li> <li><i><a href="/wiki/Karanapaddhati" title="Karanapaddhati">Karanapaddhati</a></i></li> <li><i><a href="/wiki/L%C4%ABl%C4%81vat%C4%AB" title="Līlāvatī">Līlāvatī</a></i></li> <li><i><a href="/wiki/Lokavibhaga" title="Lokavibhaga">Lokavibhaga</a></i></li> <li><i><a href="/wiki/P%C4%81t%C4%ABga%E1%B9%87ita" title="Pātīgaṇita">Pātīgaṇita</a></i></li> <li><i><a href="/wiki/Paulisa_Siddhanta" title="Paulisa Siddhanta">Paulisa Siddhanta</a></i></li> <li><i><a href="/wiki/Var%C4%81hamihira#Pancha-Siddhantika" title="Varāhamihira">Paitamaha Siddhanta</a></i></li> <li><i><a href="/wiki/Romaka_Siddhanta" title="Romaka Siddhanta">Romaka Siddhanta</a></i></li> <li><i><a href="/wiki/Sadratnamala" title="Sadratnamala">Sadratnamala</a></i></li> <li><i><a href="/wiki/Siddh%C4%81nta_Shiromani" title="Siddhānta Shiromani">Siddhānta Shiromani</a></i></li> <li><i><a href="/wiki/Shulba_Sutras" title="Shulba Sutras">Śulba Sūtras</a></i></li> <li><i><a href="/wiki/Surya_Siddhanta" title="Surya Siddhanta">Surya Siddhanta</a></i></li> <li><i><a href="/wiki/Tantrasamgraha" title="Tantrasamgraha">Tantrasamgraha</a></i></li> <li><i><a href="/wiki/Vasishtha_Siddhanta" title="Vasishtha Siddhanta">Vasishtha Siddhanta</a></i></li> <li><i><a href="/wiki/Venvaroha" title="Venvaroha">Veṇvāroha</a></i></li> <li><i><a href="/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81" title="Yuktibhāṣā">Yuktibhāṣā</a></i></li> <li><i><a href="/wiki/Yavanajataka" title="Yavanajataka">Yavanajataka</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Pioneering<br /> innovations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi numerals</a></li> <li><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numeral system</a></li> <li>Symbol for <a href="/wiki/0" title="0">zero (0)</a></li> <li><a href="/wiki/Madhava_series" title="Madhava series">Infinite series expansions for the trigonometric functions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centres</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Kerala school of astronomy and mathematics</a></li> <li><a href="/wiki/Jantar_Mantar" title="Jantar Mantar">Jantar Mantar</a> (<a href="/wiki/Jantar_Mantar,_Jaipur" title="Jantar Mantar, Jaipur">Jaipur</a>, <a href="/wiki/Jantar_Mantar,_New_Delhi" title="Jantar Mantar, New Delhi">New Delhi</a>, <a href="/wiki/Jantar_Mantar,_Ujjain" title="Jantar Mantar, Ujjain">Ujjain</a>, <a href="/wiki/Jantar_Mantar,_Varanasi" title="Jantar Mantar, Varanasi">Varanasi</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Historians of<br /> mathematics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bapudeva_Sastri" title="Bapudeva Sastri">Bapudeva Sastri</a> (1821–1900)</li> <li><a href="/w/index.php?title=Shankar_Balakrishna_Dikshit&action=edit&redlink=1" class="new" title="Shankar Balakrishna Dikshit (page does not exist)">Shankar Balakrishna Dikshit</a> (1853–1898)</li> <li><a href="/wiki/Sudhakara_Dvivedi" title="Sudhakara Dvivedi">Sudhakara Dvivedi</a> (1855–1910)</li> <li><a href="/w/index.php?title=M._Rangacarya&action=edit&redlink=1" class="new" title="M. Rangacarya (page does not exist)">M. Rangacarya</a> (1861–1916)</li> <li><a href="/wiki/P._C._Sengupta" class="mw-redirect" title="P. C. Sengupta">P. C. Sengupta</a> (1876–1962)</li> <li><a href="/wiki/B._B._Datta" class="mw-redirect" title="B. B. Datta">B. B. Datta</a> (1888–1958)</li> <li><a href="/wiki/Takao_Hayashi" title="Takao Hayashi">T. Hayashi</a></li> <li><a href="/w/index.php?title=A._A._Krishnaswamy_Ayyangar&action=edit&redlink=1" class="new" title="A. A. Krishnaswamy Ayyangar (page does not exist)">A. A. Krishnaswamy Ayyangar</a> (1892– 1953)</li> <li><a href="/wiki/Avadhesh_Narayan_Singh" title="Avadhesh Narayan Singh">A. N. Singh</a> (1901–1954)</li> <li><a href="/wiki/C._T._Rajagopal" class="mw-redirect" title="C. T. Rajagopal">C. T. Rajagopal</a> (1903–1978)</li> <li><a href="/wiki/T._A._Saraswati_Amma" class="mw-redirect" title="T. A. Saraswati Amma">T. A. Saraswati Amma</a> (1918–2000)</li> <li><a href="/w/index.php?title=S._N._Sen&action=edit&redlink=1" class="new" title="S. N. Sen (page does not exist)">S. N. Sen</a> (1918–1992)</li> <li><a href="/wiki/K._S._Shukla" class="mw-redirect" title="K. S. Shukla">K. S. Shukla</a> (1918–2007)</li> <li><a href="/wiki/K._V._Sarma" title="K. V. Sarma">K. V. Sarma</a> (1919–2005)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Translators</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Walter_Eugene_Clark" title="Walter Eugene Clark">Walter Eugene Clark</a></li> <li><a href="/wiki/Henry_Thomas_Colebrooke" title="Henry Thomas Colebrooke">Henry Thomas Colebrooke </a></li> <li><a href="/wiki/David_Pingree" title="David Pingree">David Pingree</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other regions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_mathematics" title="Babylonian mathematics">Babylon</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a></li> <li><a href="/wiki/Greek_mathematics" title="Greek mathematics">Greece</a></li> <li><a href="/wiki/Mathematics_in_the_medieval_Islamic_world" title="Mathematics in the medieval Islamic world">Islamic mathematics</a></li> <li><a href="/wiki/History_of_mathematics#Medieval_European_mathematics" title="History of mathematics">Europe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Modern<br /> institutions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indian_Statistical_Institute" title="Indian Statistical Institute">Indian Statistical Institute</a></li> <li><a href="/wiki/Bhaskaracharya_Pratishthana" title="Bhaskaracharya Pratishthana">Bhaskaracharya Pratishthana</a></li> <li><a href="/wiki/Chennai_Mathematical_Institute" title="Chennai Mathematical Institute">Chennai Mathematical Institute</a></li> <li><a href="/wiki/Institute_of_Mathematical_Sciences,_Chennai" title="Institute of Mathematical Sciences, Chennai">Institute of Mathematical Sciences</a></li> <li><a href="/wiki/Indian_Institute_of_Science" title="Indian Institute of Science">Indian Institute of Science</a></li> <li><a href="/wiki/Harish-Chandra_Research_Institute" title="Harish-Chandra Research Institute">Harish-Chandra Research Institute</a></li> <li><a href="/wiki/Homi_Bhabha_Centre_for_Science_Education" title="Homi Bhabha Centre for Science Education">Homi Bhabha Centre for Science Education</a></li> <li><a href="/wiki/Ramanujan_Institute_for_Advanced_Study_in_Mathematics" title="Ramanujan Institute for Advanced Study in Mathematics">Ramanujan Institute for Advanced Study in Mathematics</a></li> <li><a href="/wiki/Tata_Institute_of_Fundamental_Research" title="Tata Institute of Fundamental Research">TIFR</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Indian_astronomy" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Indian_astronomy" title="Template:Indian astronomy"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Indian_astronomy" title="Template talk:Indian astronomy"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Indian_astronomy" title="Special:EditPage/Template:Indian astronomy"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Indian_astronomy" style="font-size:114%;margin:0 4em"><a href="/wiki/Indian_astronomy" title="Indian astronomy">Indian astronomy</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Astronomers</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Apastamba" class="mw-redirect" title="Apastamba">Apastamba</a></li> <li><a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata I</a></li> <li><a href="/wiki/Aryabhata_II" title="Aryabhata II">Aryabhata II</a></li> <li><a href="/wiki/Vainu_Bappu" title="Vainu Bappu">Vainu Bappu</a></li> <li><a href="/wiki/Bh%C4%81skara_I" title="Bhāskara I">Bhāskara I</a></li> <li><a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a></li> <li><a href="/wiki/Baudhayana" class="mw-redirect" title="Baudhayana">Baudhayana</a></li> <li><a href="/wiki/Brahmagupta" title="Brahmagupta">Brahmagupta</a></li> <li><a href="/wiki/Sandip_Chakrabarti" title="Sandip Chakrabarti">Sandip Chakrabarti</a></li> <li><a href="/wiki/Radhagobinda_Chandra" class="mw-redirect" title="Radhagobinda Chandra">Radhagobinda Chandra</a></li> <li><a href="/wiki/Subrahmanyan_Chandrasekhar" title="Subrahmanyan Chandrasekhar">Subrahmanyan Chandrasekhar</a></li> <li><a href="/wiki/Amil_Kumar_Das" class="mw-redirect" title="Amil Kumar Das">Amil Kumar Das</a></li> <li><a href="/wiki/P_Devadas" class="mw-redirect" title="P Devadas">P. Devadas</a></li> <li><a href="/wiki/Gautama_Siddha" title="Gautama Siddha">Gautama Siddha</a></li> <li><a href="/wiki/M_K_Das_Gupta" class="mw-redirect" title="M K Das Gupta">M. K. Das Gupta</a></li> <li><a href="/wiki/Jyesthadeva" class="mw-redirect" title="Jyesthadeva">Jyesthadeva</a></li> <li><a href="/wiki/Kamalakara" title="Kamalakara">Kamalakara</a></li> <li><a href="/wiki/Katyayana" class="mw-redirect" title="Katyayana">Katyayana</a></li> <li><a href="/wiki/Lagadha" class="mw-redirect" title="Lagadha">Lagadha</a></li> <li><a href="/wiki/Lalla" title="Lalla">Lalla</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava of Sangamagrama</a></li> <li><a href="/wiki/Prasanta_Chandra_Mahalanobis" title="Prasanta Chandra Mahalanobis">Prasanta Chandra Mahalanobis</a></li> <li><a href="/wiki/Mahavira_(mathematician)" class="mw-redirect" title="Mahavira (mathematician)">Mahavira</a></li> <li><a href="/wiki/Manava" title="Manava">Manava</a></li> <li><a href="/wiki/Jayant_Narlikar" title="Jayant Narlikar">Jayant Narlikar</a></li> <li><a href="/wiki/Parameshvara" class="mw-redirect" title="Parameshvara">Parameshvara</a></li> <li><a href="/wiki/Achyuta_Pisharati" class="mw-redirect" title="Achyuta Pisharati">Achyuta Pisharati</a></li> <li><a href="/wiki/Venkatraman_Radhakrishnan" title="Venkatraman Radhakrishnan">Venkatraman Radhakrishnan</a></li> <li><a href="/wiki/J._J._Rawal" class="mw-redirect" title="J. J. Rawal">J. J. Rawal</a></li> <li><a href="/wiki/Megh_Nad_Saha" class="mw-redirect" title="Megh Nad Saha">Megh Nad Saha</a></li> <li><a href="/wiki/Jagannatha_Samrat" title="Jagannatha Samrat">Jagannatha Samrat</a></li> <li><a href="/wiki/Bapudeva_Sastri" title="Bapudeva Sastri">Bapudeva Sastri</a></li> <li><a href="/wiki/Jai_Singh_II_of_Amber" class="mw-redirect" title="Jai Singh II of Amber">Jai Singh II of Amber</a></li> <li><a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nilakantha Somayaji</a></li> <li><a href="/wiki/Sripati" class="mw-redirect" title="Sripati">Sripati</a></li> <li><a href="/wiki/Mahendra_Suri" class="mw-redirect" title="Mahendra Suri">Mahendra Suri</a></li> <li><a href="/wiki/Govind_Swarup" title="Govind Swarup">Govind Swarup</a></li> <li><a href="/wiki/Utpala_(astronomer)" title="Utpala (astronomer)">Utpala</a></li> <li><a href="/wiki/Varahamihira" class="mw-redirect" title="Varahamihira">Varahamihira</a></li> <li><a href="/wiki/Shankara_Variyar" class="mw-redirect" title="Shankara Variyar">Shankara Variyar</a></li> <li><a href="/wiki/Vasistha" class="mw-redirect" title="Vasistha">Vasistha</a></li> <li><a href="/wiki/Yajnavalkya" title="Yajnavalkya">Yajnavalkya</a></li> <li><a href="/wiki/Pathani_Samanta" title="Pathani Samanta">Pathani Samanta</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Aryabhatiya" title="Aryabhatiya">Aryabhatiya</a></i></li> <li><i><b><a href="/wiki/Brahmana" title="Brahmana">Brahmanas</a></b></i> <ul><li><i><a href="/wiki/Aitareya_Brahmana" title="Aitareya Brahmana">Aitareya Brahmana</a></i></li> <li><i><a href="/wiki/Shatapatha_Brahmana" title="Shatapatha Brahmana">Shatapatha Brahmana</a></i></li></ul></li> <li><i><span title="International Alphabet of Sanskrit transliteration"><i lang="sa-Latn"><a href="/wiki/B%E1%B9%9Bhat_Sa%E1%B9%83hit%C4%81" title="Bṛhat Saṃhitā">Bṛhat Saṃhitā</a></i></span></i></li> <li><i><a href="/wiki/Ganitagannadi" title="Ganitagannadi">Ganitagannadi</a></i></li> <li><i><a href="/wiki/Jyotirmimamsa" title="Jyotirmimamsa">Jyotirmimamsa</a></i></li> <li><i><a href="/wiki/Shulba_Sutras" title="Shulba Sutras">Shulba Sutras</a></i></li> <li><i><a href="/wiki/Panchangam" title="Panchangam">Panchangam</a></i></li> <li><i><a href="/wiki/Khandakhadyaka" title="Khandakhadyaka">Khandakhadyaka</a></i></li> <li><i><a href="/wiki/Mahadevi_(astronomy_book)" title="Mahadevi (astronomy book)">Mahādevī</a></i></li> <li><i><a href="/wiki/Makarandasarini" title="Makarandasarini">Makarandasarini</a></i></li> <li><i><b><a href="/wiki/Siddhanta_(astronomy)" class="mw-redirect" title="Siddhanta (astronomy)">Siddhantas</a></b></i> <ul><li><i><a href="/wiki/Br%C4%81hmasphu%E1%B9%ADasiddh%C4%81nta" title="Brāhmasphuṭasiddhānta">Brāhmasphuṭasiddhānta</a></i></li> <li><i><a href="/wiki/Maha-Siddhanta" class="mw-redirect" title="Maha-Siddhanta">Maha-Siddhanta</a></i></li> <li><i><a href="/wiki/Pancha-siddhantika" title="Pancha-siddhantika">Pancha-Siddhantika</a></i></li> <li><i><a href="/wiki/Paulisa_Siddhanta" title="Paulisa Siddhanta">Paulisa Siddhanta</a></i></li> <li><i><a href="/wiki/Paitamaha_Siddhanta" class="mw-redirect" title="Paitamaha Siddhanta">Paitamaha Siddhanta</a></i></li> <li><a href="/wiki/R%C4%81jam%E1%B9%9Bg%C4%81%E1%B9%85ka_(astronomy_book)" title="Rājamṛgāṅka (astronomy book)">Rājamṛgāṅka (astronomy book)</a></li> <li><i><a href="/wiki/Romaka_Siddhanta" title="Romaka Siddhanta">Romaka Siddhanta</a></i></li> <li><i><a href="/wiki/Surya_Siddhanta" title="Surya Siddhanta">Surya Siddhanta</a></i></li> <li><i><a href="/wiki/Vasishtha_Siddhanta" title="Vasishtha Siddhanta">Vasishtha Siddhanta</a></i></li></ul></li> <li><i><a href="/wiki/Tantrasangraha" class="mw-redirect" title="Tantrasangraha">Tantrasangraha</a></i></li> <li><i><a href="/wiki/Treatise_on_Astrology_of_the_Kaiyuan_Era" title="Treatise on Astrology of the Kaiyuan Era">Treatise on Astrology of the Kaiyuan Era</a></i></li> <li><i><a href="/wiki/V%C4%81kyakara%E1%B9%87a" title="Vākyakaraṇa">Vākyakaraṇa</a></i></li> <li><i><a href="/wiki/Vedanga_Jyotisha" title="Vedanga Jyotisha">Vedanga Jyotisha</a></i></li> <li><i><b><a href="/wiki/Vedas" title="Vedas">Vedas</a></b></i> <ul><li><i><a href="/wiki/Atharvaveda" title="Atharvaveda">Atharvaveda</a></i></li> <li><i><a href="/wiki/Rigveda" title="Rigveda">Rigveda</a></i></li></ul></li> <li><i><a href="/wiki/Yavanajataka" title="Yavanajataka">Yavanajataka</a></i></li> <li><i><a href="/wiki/Zij" title="Zij">Zij</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Instruments</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Armillary_sphere" title="Armillary sphere">Armillary sphere</a></li> <li><a href="/wiki/Astrolabe" title="Astrolabe">Astrolabe</a></li> <li><a href="/wiki/Armillary_sphere" title="Armillary sphere">Celestial globe</a></li> <li><a href="/wiki/Compass" title="Compass">Compass</a></li> <li><a href="/wiki/Jacob%27s_staff" title="Jacob's staff">Cross-staff</a></li> <li><a href="/wiki/Dioptra" title="Dioptra">Dioptra</a></li> <li><a href="/wiki/Equatorial_ring" title="Equatorial ring">Equatorial ring</a></li> <li><a href="/wiki/Equatorial_sundial" class="mw-redirect" title="Equatorial sundial">Equatorial sundial</a></li> <li><a href="/wiki/Globe" title="Globe">Globe</a></li> <li><a href="/wiki/Gnomon" title="Gnomon">Gnomon</a></li> <li><a href="/wiki/Mural_instrument" title="Mural instrument">Mural instrument</a></li> <li><a href="/wiki/Quadrant_(instrument)" title="Quadrant (instrument)">Quadrant</a></li> <li><a href="/wiki/Sextant_(astronomical)" class="mw-redirect" title="Sextant (astronomical)">Sextant</a></li> <li><a href="/wiki/Sundial" title="Sundial">Sundial</a></li> <li><a href="/wiki/Triquetrum_(astronomy)" title="Triquetrum (astronomy)">Triquetrum</a></li> <li><a href="/wiki/Water_clock" title="Water clock">Water clock</a></li> <li><a href="/wiki/Yantraraja" title="Yantraraja">Yantraraja</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axial_tilt" title="Axial tilt">Axial tilt</a></li> <li><a href="/wiki/Azimuth" title="Azimuth">Azimuth</a></li> <li><a href="/wiki/Cardinal_direction" title="Cardinal direction">Cardinal direction</a></li> <li><a href="/wiki/Celestial_equator" title="Celestial equator">Celestial equator</a></li> <li><a href="/wiki/Celestial_sphere" title="Celestial sphere">Celestial sphere</a></li> <li><a href="/wiki/Celestial_spheres" title="Celestial spheres">Celestial spheres</a></li> <li><a href="/wiki/Center_of_mass" title="Center of mass">Center of mass</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular orbit</a></li> <li><a href="/wiki/Deferent_and_epicycle" title="Deferent and epicycle">Deferent and epicycle</a></li> <li><a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a></li> <li><a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><a href="/wiki/Ecliptic" title="Ecliptic">Ecliptic</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a></li> <li><a href="/wiki/Equant" title="Equant">Equant</a></li> <li><a href="/wiki/Geocentric_model" title="Geocentric model">Geocentrism</a></li> <li><a href="/wiki/Tychonic_system" title="Tychonic system">Geoheliocentrism</a></li> <li><a href="/wiki/Globe" title="Globe">Globe</a></li> <li><a href="/wiki/Gravitation" class="mw-redirect" title="Gravitation">Gravity</a></li> <li><a href="/wiki/Heliocentrism" title="Heliocentrism">Heliocentrism</a></li> <li><a href="/wiki/Hindu_units_of_time" title="Hindu units of time">Hindu units of time</a></li> <li><span title="International Alphabet of Sanskrit transliteration"><i lang="sa-Latn"><a href="/wiki/Jyoti%E1%B9%A3a" class="mw-redirect" title="Jyotiṣa">Jyotiṣa</a></i></span></li> <li><a href="/wiki/Kali_ahargana" title="Kali ahargana">Kali ahargaṇa</a></li> <li><b><a href="/wiki/Kalpa_(aeon)" class="mw-redirect" title="Kalpa (aeon)">Kalpa</a></b></li> <li><a href="/wiki/Karana_(pancanga)" class="mw-redirect" title="Karana (pancanga)">Karana</a></li> <li><a href="/wiki/Manvantara" title="Manvantara">Manvantara</a></li> <li><a href="/wiki/Moonlight" title="Moonlight">Moonlight</a></li> <li><a href="/wiki/Nakshatra" title="Nakshatra">Nakshatra</a></li> <li><a href="/wiki/Nityayoga" title="Nityayoga">Nityayoga</a></li> <li><a href="/wiki/Parallax" title="Parallax">Parallax</a></li> <li><a href="/wiki/Precession" title="Precession">Precession</a></li> <li><a href="/wiki/Ritu_(Indian_season)" class="mw-redirect" title="Ritu (Indian season)">Ritu</a></li> <li><a href="/wiki/Spherical_Earth" title="Spherical Earth">Spherical Earth</a></li> <li><a href="/wiki/Sunlight" title="Sunlight">Sunlight</a></li> <li><a href="/wiki/Tithi" title="Tithi">Tithi</a></li> <li><a href="/wiki/V%C4%81ra_(astronomy)" title="Vāra (astronomy)">Vāra</a></li> <li><b><a href="/wiki/Yuga" title="Yuga">Yuga</a></b></li> <li><a href="/wiki/Astrological_sign" title="Astrological sign">Zodiacal sign</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Centres</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Jantar_Mantar" title="Jantar Mantar">Jantar Mantar</a> <ul><li><a href="/wiki/Jantar_Mantar,_Jaipur" title="Jantar Mantar, Jaipur">Jaipur</a></li> <li><a href="/wiki/Jantar_Mantar,_New_Delhi" title="Jantar Mantar, New Delhi">New Delhi</a></li> <li><a href="/wiki/Jantar_Mantar,_Ujjain" title="Jantar Mantar, Ujjain">Ujjain</a></li> <li><a href="/wiki/Jantar_Mantar,_Varanasi" title="Jantar Mantar, Varanasi">Varanasi</a></li></ul></li> <li><a class="mw-selflink selflink">Kerala school of astronomy and mathematics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other regions</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">Babylonian astronomy</a></li> <li><a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">Ancient Greek astronomy</a></li> <li><a href="/wiki/Ancient_Greek_astronomy#Hellenistic_astronomy" title="Ancient Greek astronomy">Hellenistic astronomy</a></li> <li><a href="/wiki/Astronomy_in_medieval_Islam" class="mw-redirect" title="Astronomy in medieval Islam">Islamic astronomy</a></li> <li><a href="/wiki/Chinese_astronomy" title="Chinese astronomy">Chinese astronomy</a></li> <li><a href="/wiki/Science_in_Medieval_Western_Europe" class="mw-redirect" title="Science in Medieval Western Europe">European astronomy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Months of the<br /><a href="/wiki/Hindu_calendar" title="Hindu calendar">Vedic calendar</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ol><li><a href="/wiki/Chaitra" title="Chaitra">Chaitra</a></li> <li><a href="/wiki/Vaisakha" title="Vaisakha">Vaisakha</a></li> <li><a href="/wiki/Jyeshtha_(month)" title="Jyeshtha (month)">Jyeshta</a></li> <li><a href="/wiki/Aashaadha" class="mw-redirect" title="Aashaadha">Aashaadha</a></li> <li><a href="/wiki/Shraavana" class="mw-redirect" title="Shraavana">Shraavana</a></li> <li><a href="/wiki/Bhaadra" class="mw-redirect" title="Bhaadra">Bhadrapada</a></li> <li><a href="/wiki/Ashvin_(month)" title="Ashvin (month)">Ashvin</a></li> <li><a href="/wiki/Kartika_(month)" class="mw-redirect" title="Kartika (month)">Kartik</a></li> <li><a href="/wiki/Agrahayana" title="Agrahayana"> Margashirsha</a></li> <li><a href="/wiki/Pausha" title="Pausha">Pausha</a></li> <li><a href="/wiki/Maagha" class="mw-redirect" title="Maagha">Maagha</a></li> <li><a href="/wiki/Phalguna" title="Phalguna">Phalguna</a></li></ol> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Kerala_school_of_astronomy_and_mathematics" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Kerala_School" title="Template:Kerala School"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Kerala_School" title="Template talk:Kerala School"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Kerala_School" title="Special:EditPage/Template:Kerala School"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Kerala_school_of_astronomy_and_mathematics" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Kerala school of astronomy and mathematics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Astronomers<br />and mathematicians</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_astronomers_and_mathematicians_of_the_Kerala_school" title="List of astronomers and mathematicians of the Kerala school">(Complete list)</a></li> <li><a href="/wiki/Achyutha_Pisharadi" class="mw-redirect" title="Achyutha Pisharadi">Acyuta Piṣāraṭi</a></li> <li><a href="/wiki/Azhvanchery_Thamprakkal" title="Azhvanchery Thamprakkal">Azhvāñceri Taṃprākkaḷ</a></li> <li><a href="/wiki/Chitrabhanu_(mathematician)" title="Chitrabhanu (mathematician)">Citrabhānu</a></li> <li><a href="/wiki/Damodara" title="Damodara">Dāmodara of Vațaśreņi</a></li> <li><a href="/wiki/Dev%C4%81c%C4%81rya" title="Devācārya">Devācārya</a></li> <li><a href="/wiki/Govinda_Bhattathiri" title="Govinda Bhattathiri">Govinda Bhattathiri</a></li> <li><a href="/wiki/Govindasvamin" class="mw-redirect" title="Govindasvamin">Govindasvāmin</a></li> <li><a href="/wiki/Haridatta" title="Haridatta">Haridatta</a></li> <li><a href="/wiki/Jye%E1%B9%A3%E1%B9%ADhadeva" title="Jyeṣṭhadeva">Jyeṣṭhadeva</a></li> <li><a href="/wiki/Kochukrishnan_Asan" title="Kochukrishnan Asan">Kochukrishnan Asan</a></li> <li><a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava of Sangamagrama</a></li> <li><a href="/wiki/Mazhama%E1%B9%85gala%E1%B9%83_N%C4%81r%C4%81ya%E1%B9%87an_Na%E1%B9%83p%C5%ABtiri" title="Mazhamaṅgalaṃ Nārāyaṇan Naṃpūtiri">Mazhamaṅgalaṃ Nārāyaṇan Naṃpūtiri</a></li> <li><a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nīlakaņțha Sōmayāji</a></li> <li><a href="/wiki/Kanakkusaram" title="Kanakkusaram">Nīlakaṇṭha II</a></li> <li><a href="/wiki/Parameshvara_Nambudiri" title="Parameshvara Nambudiri">Parameśvara of Vațaśśeri</a></li> <li><a href="/wiki/%C5%9Aa%E1%B9%85karan%C4%81r%C4%81ya%E1%B9%87a" title="Śaṅkaranārāyaṇa">Śaṅkaranārāyaṇa</a></li> <li><a href="/wiki/Mazhama%E1%B9%85gala%E1%B9%83_%C5%9Aa%E1%B9%85karan_Na%E1%B9%83p%C5%ABtiri" title="Mazhamaṅgalaṃ Śaṅkaran Naṃpūtiri">Śaṅkara of Mahiṣamaṅgalam</a></li> <li><a href="/wiki/Puthumana_Somayaji" title="Puthumana Somayaji">Putumana Somayāji</a></li> <li><a href="/wiki/Sankara_Variar" title="Sankara Variar">Śankara Vāriyar</a></li> <li><a href="/wiki/Sankara_Varman" title="Sankara Varman">Śaṅkara Varma of Kaṭattanāṭ</a></li> <li><a href="/wiki/Udayadiv%C4%81kara" title="Udayadivākara">Udayadivākara</a></li> <li><a href="/wiki/Vararuci" class="mw-redirect" title="Vararuci">Vararuci I</a></li> <li><a href="/wiki/Vidyamadhava" title="Vidyamadhava">Vidyamadhava</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Treatises</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Aryabhatiya-bhashya (<a href="/wiki/Nilakantha_Somayaji" title="Nilakantha Somayaji">Nīlakaņțha Sōmayāji</a>)</li> <li>Candrachayaganita</li> <li>Dasādhyāyi</li> <li><a href="/wiki/Drigganita" title="Drigganita">Drigganita</a></li> <li>Dṛkkaraṇa</li> <li>Gaṇitayuktayah</li> <li>Golavada</li> <li>Golasara</li> <li>Grahacāraṇinibandhana</li> <li>Jātaka-sāara-saṃgraha</li> <li><a href="/wiki/Jyotirmimamsa" title="Jyotirmimamsa">Jyotirmimamsa</a></li> <li>Jyotiśśāstra-saṃgraha</li> <li><a href="/wiki/Kanakkusaram" title="Kanakkusaram">Kanakkusāraṃ</a></li> <li><a href="/wiki/Karanapaddhati" title="Karanapaddhati">Karaṇapaddhati</a></li> <li><a href="/wiki/Kriyakramakari" title="Kriyakramakari">Kriyakramakari</a></li> <li>Laghuvivṛti (commentary on <a href="/wiki/Tantrasamgraha" title="Tantrasamgraha">Tantrasamgraha</a>)</li> <li>Madhyamanayanaprakara</li> <li>Mahābhāskarīya Bhāshya</li> <li><a href="/wiki/Pa%C3%B1cabodha" title="Pañcabodha">Pañcabodha</a></li> <li><a href="/wiki/Sadratnamala" title="Sadratnamala">Sadratnamālā</a></li> <li>Sidhhantadarpana</li> <li>Spuṭanirṇaya</li> <li><a href="/wiki/Tantrasamgraha" title="Tantrasamgraha">Tantrasamgraha</a></li> <li><a href="/wiki/Venvaroha" title="Venvaroha">Venvaroha</a></li> <li><a href="/wiki/Yuktibh%C4%81%E1%B9%A3%C4%81" title="Yuktibhāṣā">Yuktibhāṣā</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts/Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chandravakyas" title="Chandravakyas">Chandravakyas</a></li> <li><a href="/wiki/Drigganita" title="Drigganita">Drigganita system</a></li> <li><a href="/wiki/Katapayadi_system" title="Katapayadi system">Kaṭapayādi system</a></li> <li><a href="/wiki/Madhava%27s_correction_terms" class="mw-redirect" title="Madhava's correction terms">Madhava's correction terms</a></li> <li><a href="/wiki/Madhava_series" title="Madhava series">Madhava series</a></li> <li><a href="/wiki/Madhava%27s_sine_table" title="Madhava's sine table">Madhava's sine table</a></li> <li><a href="/wiki/Parahita" title="Parahita">Parahita system</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Places associated with<br />members of the school</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Athavanad" title="Athavanad">Athavanad</a> (Azhvanchery Thamprakkal)</li> <li><a href="/wiki/Alattiyur,_Malappuram" title="Alattiyur, Malappuram">Alathiyur</a> (Govinda Bhattathiri, etc)</li> <li><a href="/wiki/Kadathanadu" title="Kadathanadu">Kadathanadu</a> (Sankara Varman)</li> <li><a href="/wiki/Kodungallur" title="Kodungallur">Mahodayapuram (Kodungallur)</a> (Sankaranarayana)</li> <li><a href="/wiki/Kudallur" title="Kudallur">Kudallur</a> (Madhava of Sangamagrama)</li> <li><a href="/wiki/Peruvanam" title="Peruvanam">Peruvanam</a> (Mahishamangalam Sankaran Namputhiri)</li> <li><a href="/wiki/Thrikkandiyur" class="mw-redirect" title="Thrikkandiyur">Thrikkandiyur</a> (Nilakantha Somayaji, etc)</li> <li><a href="/wiki/Thrissur" title="Thrissur">Sivapuram (Thrissur)</a> (Putumana Somayaji, etc)</li> <li><a href="/wiki/Tirunavaya" title="Tirunavaya">Tirunavaya</a> (Haridatta)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Ancient_Dharmic_centres_of_higher_learning" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Ancient_Dharmic_centres_of_higher_learning" title="Template:Ancient Dharmic centres of higher learning"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Ancient_Dharmic_centres_of_higher_learning" title="Template talk:Ancient Dharmic centres of higher learning"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Ancient_Dharmic_centres_of_higher_learning" title="Special:EditPage/Template:Ancient Dharmic centres of higher learning"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Ancient_Dharmic_centres_of_higher_learning" style="font-size:114%;margin:0 4em">Ancient <a href="/wiki/Dharmic_religions" class="mw-redirect" title="Dharmic religions">Dharmic</a> centres of higher learning</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major centres of learning</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b><a href="/wiki/Nalanda" class="mw-redirect" title="Nalanda">Nalanda</a></b></li> <li><b><a href="/wiki/Nagarjunakonda" title="Nagarjunakonda">Nagarjunakonda</a></b></li> <li><b><a href="/wiki/Nandadirghi_Mahavihara" title="Nandadirghi Mahavihara">Nandadirghi</a></b></li> <li><b><a href="/wiki/Odantapuri" title="Odantapuri">Odantapuri</a></b></li> <li><b><a href="/wiki/Pushpagiri_Vihara" title="Pushpagiri Vihara">Pushpagiri</a></b></li> <li><b><a href="/wiki/Raktamrittika_Mahavihara" title="Raktamrittika Mahavihara">Raktamrittika</a></b></li> <li><b><a href="/wiki/Somapura_Mahavihara" title="Somapura Mahavihara">Somapura</a></b></li> <li><b><a href="/wiki/Taxila" title="Taxila">Taxila</a></b></li> <li><b><a href="/wiki/Vallabhi_University" class="mw-redirect" title="Vallabhi University">Vallabhi</a></b></li> <li><b><a href="/wiki/Vikramashila" title="Vikramashila">Vikramashila</a></b></li> <li><b><a href="/wiki/Jagaddala_Mahavihara" title="Jagaddala Mahavihara">Jagaddala</a></b></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other centres of learning</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ajanta_Caves" title="Ajanta Caves">Ajanta</a></li> <li><a href="/wiki/Bikrampur_Vihara" title="Bikrampur Vihara">Bikrampur Vihara</a></li> <li><a href="/wiki/Kanchipuram" title="Kanchipuram">Kanchipuram</a></li> <li><a href="/wiki/Kanheri_Caves" title="Kanheri Caves">Kanheri</a></li> <li><a class="mw-selflink selflink">Kerala school of astronomy and mathematics</a></li> <li><a href="/wiki/Lalitgiri" title="Lalitgiri">Lalitgiri</a></li> <li><a href="/wiki/Mansar,_India" title="Mansar, India">Mansar</a></li> <li><a href="/wiki/Manyakheta" class="mw-redirect" title="Manyakheta">Manyakheta</a></li> <li><a href="/wiki/Paithan" title="Paithan">Paithan</a></li> <li><a href="/wiki/Pandit_Vihara" title="Pandit Vihara">Pandit Vihara</a></li> <li><a href="/wiki/Ratnagiri,_Odisha" title="Ratnagiri, Odisha">Ratnagiri</a></li> <li><a href="/wiki/Shalban_Vihara" title="Shalban Vihara">Shalban Vihara</a></li> <li><a href="/wiki/Sharada_Peeth" title="Sharada Peeth">Sharada Peeth</a></li> <li><a href="/wiki/Sunethradevi_Pirivena" class="mw-redirect" title="Sunethradevi Pirivena">Sunethradevi Pirivena</a></li> <li><a href="/wiki/Telhara_monastery" title="Telhara monastery">Telhara monastery</a></li> <li><a href="/wiki/Udayagiri,_Odisha" title="Udayagiri, Odisha">Udayagiri</a></li> <li><a href="/wiki/Ujjayini" class="mw-redirect" title="Ujjayini">Ujjayini</a></li> <li><a href="/wiki/Varanasi" title="Varanasi">Varanasi</a></li> <li><a href="/wiki/Vidyalankara_Pirivena" title="Vidyalankara Pirivena">Vidyalankara Pirivena</a></li> <li><a href="/wiki/Vidyodaya_Pirivena" title="Vidyodaya Pirivena">Vidyodaya Pirivena</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&oldid=1253389897">https://en.wikipedia.org/w/index.php?title=Kerala_school_of_astronomy_and_mathematics&oldid=1253389897</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a 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