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Ye (Mathematiker) – German" lang="de" hreflang="de" data-title="Li Ye (Mathematiker)" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%B9_%CE%93%CE%B9%CE%B5" title="Λι Γιε – Greek" lang="el" hreflang="el" data-title="Λι Γιε" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Li_Ye" title="Li Ye – Spanish" lang="es" hreflang="es" data-title="Li Ye" 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/Li_Ye_(math%C3%A9maticien)" title="Li Ye (mathématicien) – French" lang="fr" hreflang="fr" data-title="Li Ye (mathématicien)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%9D%8E%E5%86%B6" title="李冶 – Japanese" lang="ja" hreflang="ja" data-title="李冶" 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-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Li_Ye" title="Li Ye – Romanian" lang="ro" hreflang="ro" data-title="Li Ye" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%B8_%D0%95_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)" title="Ли Е (математик) – 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.hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">In this <a href="/wiki/Chinese_name" title="Chinese name">Chinese name</a>, the <a href="/wiki/Chinese_surname" title="Chinese surname">family name</a> is <i> <a href="/wiki/Li_(surname_%E6%9D%8E)" title="Li (surname 李)">Li</a></i>.</div> <div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Chinese scientist and writer (1192–1279)</div> <p><b>Li Ye</b> (<a href="/wiki/Chinese_language" title="Chinese language">Chinese</a>: <span lang="zh">李冶</span>; <a href="/wiki/Wade%E2%80%93Giles" title="Wade–Giles">Wade–Giles</a>: <i><span lang="zh-Latn-wadegile"><i><b>Li Yeh</b></i></span></i>; 1192–1279), born <b>Li Zhi</b> (Chinese: <span lang="zh">李治</span>), <a href="/wiki/Courtesy_name" title="Courtesy name">courtesy name</a> <b>Li Jingzhai</b> (Chinese: <span lang="zh">李敬斋</span>),<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-0" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-IdRef_2-0" class="reference"><a href="#cite_note-IdRef-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> was a Chinese mathematician, politician, and writer who published and improved the <a href="/wiki/Tian_yuan_shu" title="Tian yuan shu">tian yuan shu</a> method for solving <a href="/wiki/Polynomial_equation" class="mw-redirect" title="Polynomial equation">polynomial equations</a> of one variable.<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-1" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-MacTutor_3-0" class="reference"><a href="#cite_note-MacTutor-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Ho_book_4-0" class="reference"><a href="#cite_note-Ho_book-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Scientific_Biography_5-0" class="reference"><a href="#cite_note-Scientific_Biography-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Lam_6-0" class="reference"><a href="#cite_note-Lam-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Vita_7-0" class="reference"><a href="#cite_note-Vita-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Along with the 4th-century Chinese astronomer <a href="/wiki/Yu_Xi" title="Yu Xi">Yu Xi</a>, Li Ye proposed the idea of a <a href="/wiki/Spherical_Earth" title="Spherical Earth">spherical Earth</a> instead of a <a href="/wiki/Flat_Earth" title="Flat Earth">flat one</a> before the advances of European science in the 17th century. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Name">Name</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=1" title="Edit section: Name"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li Ye was born Li Zhi, but later changed his name to Li Ye to <a href="/wiki/Naming_taboo" title="Naming taboo">avoid confusion</a> with the <a href="/wiki/Emperor_Gaozong_of_Tang" title="Emperor Gaozong of Tang">third Tang emperor</a> who was also named Li Zhi, removing one stroke from his original name to change the character. His name is also sometimes written as Li Chih or Li Yeh. His literary name was Renqing (<a href="/wiki/Chinese_language" title="Chinese language">Chinese</a>: <span lang="zh">仁卿</span>; <a href="/wiki/Wade%E2%80%93Giles" title="Wade–Giles">Wade–Giles</a>: <i><span lang="zh-Latn-wadegile">Jen-ch’ing</span></i>) and his <a href="/wiki/Art-name" class="mw-redirect" title="Art-name">appellation</a> was Jingzhai (<a href="/wiki/Chinese_language" title="Chinese language">Chinese</a>: <span lang="zh">敬斋</span>; <a href="/wiki/Wade%E2%80%93Giles" title="Wade–Giles">Wade–Giles</a>: <i><span lang="zh-Latn-wadegile">Ching-chai</span></i>).<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-2" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-IdRef_2-1" class="reference"><a href="#cite_note-IdRef-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Life">Life</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=2" title="Edit section: Life"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Li Ye was born in <a href="/wiki/Daxing_District" class="mw-redirect" title="Daxing District">Daxing</a> (now Beijing). His father was a secretary to an officer in the <a href="/wiki/Jurchen_people" title="Jurchen people">Jurchen</a> army. Li passed the <a href="/wiki/Imperial_examination" title="Imperial examination">civil service examination</a> in 1230 at the age of 38, and was administrative prefect of Jun prefecture in <a href="/wiki/Henan" title="Henan">Henan</a> province until the <a href="/wiki/Mongol%E2%80%93Jin_Dynasty_War" class="mw-redirect" title="Mongol–Jin Dynasty War">Mongol invasion in 1233</a>. He then lived in poverty in the mountainous <a href="/wiki/Shanxi_province" class="mw-redirect" title="Shanxi province">Shanxi province</a>. In 1248 he finished his most known work <i>Ceyuan haijing</i> (<span title="Chinese-language text"><span lang="zh">測圓海鏡</span></span>, <i>Sea mirror of circle measurements</i>).<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-3" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Li then returned to <a href="/wiki/Hebei" title="Hebei">Hebei</a>. </p><p>In 1257, <a href="/wiki/Kublai_Khan" title="Kublai Khan">Kublai Khan</a>, grandson of <a href="/wiki/Genghis_Khan" title="Genghis Khan">Genghis Khan</a>, ordered Li to give advice on science. In 1259, Li completed <i>Yigu yanduan</i> (<span title="Chinese-language text"><span lang="zh">益古演段</span></span>, <i>New steps in computation</i>), also a mathematics text. After becoming <a href="/wiki/Khan_(title)" title="Khan (title)">Khan</a>, Kublai twice offered Li government positions, but Li was too old and in ill health. In 1264, Li finally accepted a position at the <a href="/wiki/Hanlin_Academy" title="Hanlin Academy">Hanlin Academy</a>, writing official histories. However, he had a political fallout and resigned after a few months, again citing ill health.<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-4" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> He spent his final years teaching at his home near Feng Lung mountain in Yuan, <a href="/wiki/Hebei" title="Hebei">Hebei</a>. Li told his son to burn all of his books except for <i>Sea mirror of circle measurements</i>.<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-5" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=3" title="Edit section: Mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Ceyuan_haijing">Ceyuan haijing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=4" title="Edit section: Ceyuan haijing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Ceyuan_haijing" title="Ceyuan haijing">Ceyuan haijing</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg/300px-%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg" decoding="async" width="300" height="410" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg/450px-%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg/600px-%E5%9C%86%E5%9F%8E%E5%9B%BE%E5%BC%8F.jpg 2x" data-file-width="687" data-file-height="938" /></a><figcaption>The master figure in <i>Sea mirror of circle measurements</i>, that all the problems use. It shows a circular city wall, inscribed in a right triangle and a square.</figcaption></figure> <p><a href="/wiki/Ceyuan_haijing" title="Ceyuan haijing">Ceyuan haijing</a> (<i>Sea mirror of circle measurements</i>) is a collection of 170 problems, all related to the same example of a circular city wall inscribed in a <a href="/wiki/Right_triangle" title="Right triangle">right triangle</a> and a square.<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-6" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> They often involve two people who walk on straight lines until they can see each other, meet or reach a tree in a certain spot. The purpose of book was to study intricate geometrical relations with algebra and provide solutions to equations.<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> </p><p>Many of the problems are solved by polynomial equations, which are represented using a method called <a href="/wiki/Tian_yuan_shu" title="Tian yuan shu">tian yuan shu</a>, "coefficient array method" or literally "method of the celestial unknown".<sup id="cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-7" class="reference"><a href="#cite_note-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-needham_ling_1995_p45_11-0" class="reference"><a href="#cite_note-needham_ling_1995_p45-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The method was known before him in some form. It is a positional system of <a href="/wiki/Rod_numeral" class="mw-redirect" title="Rod numeral">rod numerals</a> to represent <a href="/wiki/Polynomial_equation" class="mw-redirect" title="Polynomial equation">polynomial equations</a>. </p><p>For example, 2x<sup>2</sup> + 18x − 316 = 0 is represented as </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Polynomial_equation_with_rod_numerals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/d/d6/Polynomial_equation_with_rod_numerals.png" decoding="async" width="152" height="122" class="mw-file-element" data-file-width="152" data-file-height="122" /></a></span> which is equal to <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Polynomial_equation_in_tian_yuan_shu_with_arabic_numerals.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/b/be/Polynomial_equation_in_tian_yuan_shu_with_arabic_numerals.png" decoding="async" width="152" height="122" class="mw-file-element" data-file-width="152" data-file-height="122" /></a></span> in Arabic Numbers. </p><p>The <span title="Chinese-language text"><span lang="zh">元</span></span> (<i>yuan</i>) denotes the unknown x, so the numerals on that line mean 18x. The line below is the constant term (-316) and the line above is the coefficient of the quadratic (x<sup>2</sup>) term. The system accommodates arbitrarily high exponents of the unknown by adding more lines on top and negative exponents by adding lines below the constant term. Decimals can also be represented. Later, the line order was reversed so that the first line is the lowest exponent. </p><p>Li does not explain how to solve equations in general, but shows it with the example problems. Most of the equations can be reduced to the second or sometimes third order. It is often assumed that he used methods similar to <a href="/wiki/Ruffini%27s_rule" title="Ruffini's rule">Ruffini's rule</a> and <a href="/wiki/Horner_scheme" class="mw-redirect" title="Horner scheme">Horner scheme</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Yigu_yanduan">Yigu yanduan</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=5" title="Edit section: Yigu yanduan"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Yigu_yanduan" title="Yigu yanduan">Yigu yanduan</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg/300px-%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg" decoding="async" width="300" height="398" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg/450px-%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg/600px-%E7%9B%8A%E5%8F%A4%E7%AC%AC%E5%85%AB%E9%97%AE.jpg 2x" data-file-width="618" data-file-height="819" /></a><figcaption>Problem 8 in Yigu yanduan</figcaption></figure> <p><a href="/wiki/Yigu_yanduan" title="Yigu yanduan">Yigu yanduan</a> (<i>New steps in computation</i>) is a work of more basic mathematics written soon after Li Ye completed Ceyuan haijing, and was probably written to help students who could not understand <i>Sea mirror of circle measurements</i>. Yigu yanduan consists of three volumes dedicated to solving geometrical problems on two tracks, through <a href="/wiki/Tian_yuan_shu" title="Tian yuan shu">Tian yuan shu</a> and geometry. It also contained algebraic problems, but with slightly different notations.<sup id="cite_ref-needham_ling_1995_p45_11-1" class="reference"><a href="#cite_note-needham_ling_1995_p45-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy_and_shape_of_the_earth">Astronomy and shape of the earth</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=6" title="Edit section: Astronomy and shape of the earth"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i>huntian</i> (<span title="Chinese-language text"><span lang="zh">渾天</span></span>) theory of the <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a> stipulated that the earth was <a href="/wiki/Flat_Earth" title="Flat Earth">flat and square</a>, while the heavens were spherical in shape, along with celestial bodies such as the sun and moon (described by 1st-century AD polymathic scientist and statesman <a href="/wiki/Zhang_Heng" title="Zhang Heng">Zhang Heng</a> like a <a href="/wiki/Crossbow" title="Crossbow">crossbow</a> bullet and ball, respectively).<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> However, the idea of a flat earth was criticized by the Jin dynasty astronomer <a href="/wiki/Yu_Xi" title="Yu Xi">Yu Xi</a> (fl. 307-345 AD), who suggested a rounded shape as an alternative.<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> In his <i>Jingzhai gu zhin zhu</i> (<span title="Chinese-language text"><span lang="zh">敬齋古今注</span></span>),<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> Li Ye echoed Yu's idea that the <a href="/wiki/Spherical_Earth" title="Spherical Earth">Earth was spherical</a>, similar in shape to the heavens but smaller in size, arguing that it could not be square since that would hinder the movement of the heavens and celestial bodies.<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> </p><p>However, the idea of a spherical earth was not accepted in mainstream Chinese science and <a href="/wiki/Chinese_cartography" class="mw-redirect" title="Chinese cartography">cartography</a> until the 17th century during the late <a href="/wiki/Ming_dynasty" title="Ming dynasty">Ming</a> and early <a href="/wiki/Qing_dynasty" title="Qing dynasty">Qing</a> periods, with the advent of evidence of European <a href="/wiki/Circumnavigation" title="Circumnavigation">circumnavigation</a> of the globe.<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> The flat Earth theory in Chinese science was finally overturned in the 17th-century. <a href="/wiki/Jesuit_China_Missions" class="mw-redirect" title="Jesuit China Missions">Jesuits in China</a> also introduced the spherical Earth model advanced by <a href="/wiki/Ancient_Greek_astronomy" title="Ancient Greek astronomy">ancient Greeks</a> such as <a href="/wiki/Philolaus" title="Philolaus">Philolaus</a> and <a href="/wiki/Eratosthenes" title="Eratosthenes">Eratosthenes</a><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> and presented in <a href="/wiki/World_map" title="World map">world maps</a> such as <a href="/wiki/Matteo_Ricci" title="Matteo Ricci">Matteo Ricci</a>'s <i><a href="/wiki/Kunyu_Wanguo_Quantu" title="Kunyu Wanguo Quantu">Kunyu Wanguo Quantu</a></i> published in <a href="/wiki/Ming_dynasty" title="Ming dynasty">Ming-dynasty</a> China in 1602.<sup id="cite_ref-Baran_18-0" class="reference"><a href="#cite_note-Baran-18"><span class="cite-bracket">[</span>18<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=Li_Ye_(mathematician)&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Chinese_astronomy" title="Chinese astronomy">Chinese astronomy</a></li> <li><a href="/wiki/Chinese_mathematics" title="Chinese mathematics">Chinese mathematics</a></li> <li><a href="/wiki/Qin_Jiushao" title="Qin Jiushao">Qin Jiushao</a></li> <li><a href="/wiki/Zhu_Shijie" title="Zhu Shijie">Zhu Shijie</a></li></ul> <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=Li_Ye_(mathematician)&action=edit&section=8" title="Edit section: References"><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-andrea_breard_encyclopaedia_britannica_january_2021-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-andrea_breard_encyclopaedia_britannica_january_2021_1-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text">Breard, Andrea. (Jan 01, 2021). "<a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Li-Ye">Li Ye: Chinese mathematician</a>". <i><a href="/wiki/Encyclopaedia_Britannica" class="mw-redirect" title="Encyclopaedia Britannica">Encyclopaedia Britannica</a></i>. Accessed 7 February 2021.</span> </li> <li id="cite_note-IdRef-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-IdRef_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-IdRef_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">"<a rel="nofollow" class="external text" href="https://www.idref.fr/185608124">Li, Ye (1192-1279) 李, 冶 (1192-1279)</a>" IdRef: <i>Identifiants et Référentials pour l'enseignement supérieur et la recherche</i> (French). Accessed 19 February 2018.</span> </li> <li id="cite_note-MacTutor-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-MacTutor_3-0">^</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="CITEREFO'ConnorRobertson2003" class="citation web cs1">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a> (December 2003). <a rel="nofollow" class="external text" href="http://www-history.mcs.st-and.ac.uk/Biographies/Li_Zhi.html">"Li Zhi Biography"</a>. <i><a href="/wiki/MacTutor_History_of_Mathematics_archive" class="mw-redirect" title="MacTutor History of Mathematics archive">MacTutor History of Mathematics archive</a></i>. University of St Andrews in Scotland<span class="reference-accessdate">. Retrieved <span class="nowrap">21 December</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MacTutor+History+of+Mathematics+archive&rft.atitle=Li+Zhi+Biography&rft.date=2003-12&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=http%3A%2F%2Fwww-history.mcs.st-and.ac.uk%2FBiographies%2FLi_Zhi.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span></span> </li> <li id="cite_note-Ho_book-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ho_book_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHo2000" class="citation book cs1">Ho, Peng Yoke (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_P6C4JO4JCUC&pg=PA89"><i>Li, Qi and Shu: An Introduction to Science and Civilization in China</i></a> (unabridged ed.). Courier Dover Publications. pp. 89–96. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-41445-0" title="Special:BookSources/0-486-41445-0"><bdi>0-486-41445-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Li%2C+Qi+and+Shu%3A+An+Introduction+to+Science+and+Civilization+in+China&rft.pages=89-96&rft.edition=unabridged&rft.pub=Courier+Dover+Publications&rft.date=2000&rft.isbn=0-486-41445-0&rft.aulast=Ho&rft.aufirst=Peng+Yoke&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_P6C4JO4JCUC%26pg%3DPA89&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span></span> </li> <li id="cite_note-Scientific_Biography-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Scientific_Biography_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHo2008" class="citation encyclopaedia cs1">Ho, Peng Yoke (2008). <a rel="nofollow" class="external text" href="http://www.encyclopedia.com/doc/1G2-2830902611.html">"Li Chih, also called Li Yeh"</a>. <i><a href="/wiki/Complete_Dictionary_of_Scientific_Biography" class="mw-redirect" title="Complete Dictionary of Scientific Biography">Complete Dictionary of Scientific Biography</a></i>. Charles Scribner's Sons<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Li+Chih%2C+also+called+Li+Yeh&rft.btitle=Complete+Dictionary+of+Scientific+Biography&rft.pub=Charles+Scribner%27s+Sons&rft.date=2008&rft.aulast=Ho&rft.aufirst=Peng+Yoke&rft_id=http%3A%2F%2Fwww.encyclopedia.com%2Fdoc%2F1G2-2830902611.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span> Via encyclopedia.com.</span> </li> <li id="cite_note-Lam-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lam_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLam_Lay-YongAng_Tian-Se1984" class="citation journal cs1">Lam Lay-Yong; Ang Tian-Se (September 1984). "Li Ye and his Yi Gu Yan Duan (old mathematics in expanded sections)". <i>Archive for History of Exact Sciences</i>. <b>29</b> (3). Berlin / Heidelberg: Springer: 237–266. <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%2FBF00348622">10.1007/BF00348622</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:120593520">120593520</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=Li+Ye+and+his+Yi+Gu+Yan+Duan+%28old+mathematics+in+expanded+sections%29&rft.volume=29&rft.issue=3&rft.pages=237-266&rft.date=1984-09&rft_id=info%3Adoi%2F10.1007%2FBF00348622&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A120593520%23id-name%3DS2CID&rft.au=Lam+Lay-Yong&rft.au=Ang+Tian-Se&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span></span> </li> <li id="cite_note-Vita-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Vita_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSwetz1996" class="citation book cs1">Swetz, Frank (1996). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=D21wKHoYGg0C&pg=PA89">"Enigmas of Chinese Mathematics"</a>. In Ronald Calinger (ed.). <i>Vita mathematica: historical research and integration with teaching</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">MAA</a> Notes. Vol. 40. Cambridge University Press. pp. 89–90. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-88385-097-4" title="Special:BookSources/0-88385-097-4"><bdi>0-88385-097-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Enigmas+of+Chinese+Mathematics&rft.btitle=Vita+mathematica%3A+historical+research+and+integration+with+teaching&rft.series=MAA+Notes&rft.pages=89-90&rft.pub=Cambridge+University+Press&rft.date=1996&rft.isbn=0-88385-097-4&rft.aulast=Swetz&rft.aufirst=Frank&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DD21wKHoYGg0C%26pg%3DPA89&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, p. 40.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, pp. 44, 129.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, pp. 44-45.</span> </li> <li id="cite_note-needham_ling_1995_p45-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-needham_ling_1995_p45_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-needham_ling_1995_p45_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, p. 45.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, pp. 216-218, 227.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, pp. 220, 498.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, p. 498; footnote i.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, p. 498.</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">Needham, Joseph; Wang, Ling. (1995) [1959]. <i>Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth</i>, vol. 3, reprint edition. Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-05801-5" title="Special:BookSources/0-521-05801-5">0-521-05801-5</a>, pp. 498-499.</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">Cullen, Christopher. (1993). "Appendix A: A Chinese Eratosthenes of the Flat Earth: a Study of a Fragment of Cosmology in Huainanzi", in Major, John. S. (ed), <i>Heaven and Earth in Early Han Thought: Chapters Three, Four, and Five of the Huananzi</i>. Albany: State University of New York Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7914-1585-6" title="Special:BookSources/0-7914-1585-6">0-7914-1585-6</a>, p. 269-270.</span> </li> <li id="cite_note-Baran-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Baran_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaran2009" class="citation news cs1">Baran, Madeleine (December 16, 2009). <a rel="nofollow" class="external text" href="http://minnesota.publicradio.org/display/web/2009/12/16/tulip-map/">"Historic map coming to Minnesota"</a>. St. Paul, Minn.: Minnesota Public Radio<span class="reference-accessdate">. Retrieved <span class="nowrap">19 February</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Historic+map+coming+to+Minnesota&rft.date=2009-12-16&rft.aulast=Baran&rft.aufirst=Madeleine&rft_id=http%3A%2F%2Fminnesota.publicradio.org%2Fdisplay%2Fweb%2F2009%2F12%2F16%2Ftulip-map%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALi+Ye+%28mathematician%29" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Li_Ye_(mathematician)&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Chan, Hok-Lam. 1997. “A Recipe to Qubilai Qa'an on Governance: The Case of Chang Te-hui and Li Chih”. Journal of the Royal Asiatic Society 7 (2). Cambridge University Press: 257–83. <a rel="nofollow" class="external free" href="https://www.jstor.org/stable/25183352">https://www.jstor.org/stable/25183352</a>.</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 .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": 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aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q716964#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q716964#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q716964#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">International</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://isni.org/isni/0000000079575819">ISNI</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://viaf.org/viaf/120999019">VIAF</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.worldcat.org/fast/176617/">FAST</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.oclc.org/worldcat/entity/E39PBJfCtYf9Dhcq7HrJXDBHG3">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/1044570636">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n85282369">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb168962696">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb168962696">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an36641011">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p141774959">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90544135">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007349813605171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:li.ye.5">zbMATH</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1355025">Trove</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/185608124">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6d80kvj">SNAC</a></span></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="Song_dynasty_topics" 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="3"><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:Song_dynasty_topics" title="Template:Song dynasty topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Song_dynasty_topics" title="Template talk:Song dynasty topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Song_dynasty_topics" title="Special:EditPage/Template:Song dynasty topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Song_dynasty_topics" style="font-size:114%;margin:0 4em"><a href="/wiki/Song_dynasty" title="Song dynasty">Song dynasty</a> topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_the_Song_dynasty" title="History of the Song dynasty">History</a> (<a href="/wiki/Timeline_of_the_Song_dynasty" title="Timeline of the Song dynasty">Timeline</a>)</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/Chenqiao_mutiny" title="Chenqiao mutiny">Chenqiao mutiny</a></li> <li>Unification <ul><li><a href="/wiki/Song_conquest_of_Later_Shu" title="Song conquest of Later Shu">Later Shu</a></li> <li><a href="/wiki/Song_conquest_of_Southern_Han" title="Song conquest of Southern Han">Southern Han</a></li> <li><a href="/wiki/Song_conquest_of_Southern_Tang" title="Song conquest of Southern Tang">Southern Tang</a></li> <li><a href="/wiki/Battle_of_Gaoliang_River" title="Battle of Gaoliang River">Gaoliang River</a></li></ul></li> <li><a href="/wiki/Song%E2%80%93%C4%90%E1%BA%A1i_C%E1%BB%93_Vi%E1%BB%87t_war" title="Song–Đại Cồ Việt war">Song–Đại Cồ Việt war</a></li> <li><a href="/wiki/Song%E2%80%93Xia_wars" title="Song–Xia wars">Song–Xia wars</a></li> <li><a href="/wiki/Chanyuan_Treaty" title="Chanyuan Treaty">Chanyuan Treaty</a></li> <li><a href="/wiki/Wang_Ze" title="Wang Ze">Wang Ze rebellion</a></li> <li><a href="/wiki/Nong_Zhigao_rebellions" title="Nong Zhigao rebellions">Nong Zhigao rebellions</a></li> <li><a href="/wiki/Song%E2%80%93Tibet_relations" title="Song–Tibet relations">Song–Tibet relations</a></li> <li><a href="/wiki/Song%E2%80%93Viet_war_(1075%E2%80%931077)" class="mw-redirect" title="Song–Viet war (1075–1077)">Song–Viet war (1075–1077)</a></li> <li><a href="/wiki/Fang_La" title="Fang La">Fang La rebellion</a></li> <li><a href="/wiki/Alliance_Conducted_at_Sea" title="Alliance Conducted at Sea">Alliance Conducted at Sea</a></li> <li><a href="/wiki/Jin%E2%80%93Song_Wars" class="mw-redirect" title="Jin–Song Wars">Jin–Song Wars</a> <ul><li><a href="/wiki/Jingkang_incident" title="Jingkang incident">Jingkang</a></li> <li><a href="/wiki/Battle_of_Huangtiandang" title="Battle of Huangtiandang">Huangtiandang</a></li> <li><a href="/wiki/Siege_of_De%27an" title="Siege of De'an">De'an</a></li> <li><a href="/wiki/Battle_of_Yancheng" title="Battle of Yancheng">Yancheng</a></li> <li><a href="/wiki/Treaty_of_Shaoxing" title="Treaty of Shaoxing">Treaty of Shaoxing</a></li> <li><a href="/wiki/Battle_of_Tangdao" title="Battle of Tangdao">Tangdao</a></li> <li><a href="/wiki/Battle_of_Caishi" title="Battle of Caishi">Caishi</a></li> <li><a href="/wiki/Siege_of_Caizhou" title="Siege of Caizhou">Caizhou</a></li></ul></li> <li><a href="/wiki/Mongol_conquest_of_Song_China" class="mw-redirect" title="Mongol conquest of Song China">Mongol conquest</a> <ul><li><a href="/wiki/Siege_of_Diaoyucheng" title="Siege of Diaoyucheng">Diaoyucheng</a></li> <li><a href="/wiki/Battle_of_Xiangyang" title="Battle of Xiangyang">Xiangyang</a></li> <li><a href="/wiki/Battle_of_Yamen" title="Battle of Yamen">Yamen</a></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Ma_Lin_Guests.jpg" class="mw-file-description" title="Painting by Song painter Ma Lin"><img alt="Painting by Song painter Ma Lin" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Ma_Lin_Guests.jpg/50px-Ma_Lin_Guests.jpg" decoding="async" width="50" height="49" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Ma_Lin_Guests.jpg/75px-Ma_Lin_Guests.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Ma_Lin_Guests.jpg/100px-Ma_Lin_Guests.jpg 2x" data-file-width="1864" data-file-height="1818" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Government</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/List_of_emperors_of_the_Song_dynasty" title="List of emperors of the Song dynasty">Emperors</a> <ul><li><a href="/wiki/Chinese_emperors_family_tree_(middle)#Song_dynasty" class="mw-redirect" title="Chinese emperors family tree (middle)">Family tree</a></li></ul></li> <li><a href="/wiki/Imperial_examination#Song_dynasty_(960–1279)" title="Imperial examination">Imperial examinations</a></li> <li><a href="/wiki/Administration_of_territory_in_dynastic_China#Song_dynasty_(960–1279)" title="Administration of territory in dynastic China">Administrative units</a> <ul><li><a href="/wiki/Sixteen_Prefectures" title="Sixteen Prefectures">Sixteen Prefectures</a></li></ul></li> <li><a href="/wiki/Military_history_of_the_Song_dynasty" title="Military history of the Song dynasty">Military</a></li> <li><a href="/wiki/Bureau_of_Military_Affairs" title="Bureau of Military Affairs">Bureau of Military Affairs</a></li> <li><a href="/wiki/Qingli_Reforms" title="Qingli Reforms">Qingli Reforms</a></li> <li><a href="/wiki/New_Policies_(Song_dynasty)" title="New Policies (Song dynasty)">New Policies</a></li> <li><a href="/wiki/Baojia_system" title="Baojia system">Baojia system</a></li> <li><a href="/wiki/Three_Bureaus" title="Three Bureaus">Three Bureaus</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Three_Departments_and_Six_Ministries" title="Three Departments and Six Ministries">Three Departments</a></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/Department_of_State_Affairs" class="mw-redirect" title="Department of State Affairs">Department of State Affairs</a></li> <li><a href="/wiki/Zhongshu_Sheng" title="Zhongshu Sheng">Secretariat</a></li> <li><a href="/wiki/Menxia_Sheng" title="Menxia Sheng">Chancellery</a></li> <li>(<a href="/wiki/Secretariat-Chancellery" title="Secretariat-Chancellery">Secretariat-Chancellery</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;"><a href="/wiki/Three_Departments_and_Six_Ministries" title="Three Departments and Six Ministries">Six Ministries</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ol><li><a href="/wiki/Ministry_of_Personnel" title="Ministry of Personnel">Ministry of Personnel</a></li> <li><a href="/wiki/Ministry_of_Revenue_(imperial_China)" title="Ministry of Revenue (imperial China)">Ministry of Revenue</a></li> <li><a href="/wiki/Ministry_of_Rites" title="Ministry of Rites">Ministry of Rites</a></li> <li><a href="/wiki/Ministry_of_War_(imperial_China)" title="Ministry of War (imperial China)">Ministry of War</a></li> <li><a href="/wiki/Ministry_of_Justice_(imperial_China)" title="Ministry of Justice (imperial China)">Ministry of Justice</a></li> <li><a href="/wiki/Ministry_of_Works_(imperial_China)" title="Ministry of Works (imperial China)">Ministry of Works</a></li></ol> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Culture_of_the_Song_dynasty" title="Culture of the Song dynasty">Culture</a> and <a href="/wiki/Society_of_the_Song_dynasty" title="Society of the Song dynasty">Society</a></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/Religion_in_the_Song_dynasty" title="Religion in the Song dynasty">Religion</a></li> <li><a href="/wiki/Song_poetry" title="Song poetry">Poetry</a></li> <li><a href="/wiki/Five_Great_Kilns" title="Five Great Kilns">Five Great Kilns</a> <ul><li><a href="/wiki/Ding_ware" title="Ding ware">Ding ware</a></li> <li><a href="/wiki/Ge_ware" title="Ge ware">Ge ware</a></li> <li><a href="/wiki/Guan_ware" title="Guan ware">Guan ware</a></li> <li><a href="/wiki/Jun_ware" title="Jun ware">Jun ware</a></li> <li><a href="/wiki/Ru_ware" title="Ru ware">Ru ware</a></li></ul></li> <li><a href="/wiki/Longquan_celadon" title="Longquan celadon">Longquan celadon</a></li> <li><a href="/wiki/Cizhou_ware" title="Cizhou ware">Cizhou ware</a></li> <li><a href="/wiki/Qingbai_ware" title="Qingbai ware">Qingbai ware</a></li> <li><a href="/wiki/Yaozhou_ware" title="Yaozhou ware">Yaozhou ware</a></li> <li><a href="/wiki/Jian_ware" title="Jian ware">Jian ware</a></li> <li><a href="/wiki/Four_Treasures_of_Hebei#Great_Bodhisattva_of_Zhengding_(971)" title="Four Treasures of Hebei">Great Bodhisattva of Zhengding</a></li> <li><i><a href="/wiki/Along_the_River_During_the_Qingming_Festival" title="Along the River During the Qingming Festival">Along the River During the Qingming Festival</a></i></li> <li><a href="/wiki/Four_Great_Books_of_Song" title="Four Great Books of Song">Four Great Books of Song</a></li> <li><i><a href="/wiki/Dongjing_Meng_Hua_Lu" title="Dongjing Meng Hua Lu">Dongjing Meng Hua Lu</a></i></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Writers</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/Fan_Zhongyan" title="Fan Zhongyan">Fan Zhongyan</a> (989–1052)</li> <li><a href="/wiki/Yan_Shu" title="Yan Shu">Yan Shu</a> (991–1055)</li> <li><a href="/wiki/Song_Qi" title="Song Qi">Song Qi</a> (998–1061)</li> <li><a href="/wiki/Mei_Yaochen" title="Mei Yaochen">Mei Yaochen</a> (1002–1060)</li> <li><a href="/wiki/Ouyang_Xiu" title="Ouyang Xiu">Ouyang Xiu</a> (1007–1072)</li> <li><a href="/wiki/Su_Xun" title="Su Xun">Su Xun</a> (1009–1066)</li> <li><a href="/wiki/Shao_Yong" title="Shao Yong">Shao Yong</a> (1011–1077)</li> <li><a href="/wiki/Cai_Xiang" title="Cai Xiang">Cai Xiang</a> (1012–1067)</li> <li><a href="/wiki/Zhou_Dunyi" title="Zhou Dunyi">Zhou Dunyi</a> (1017–1073)</li> <li><a href="/wiki/Zeng_Gong" title="Zeng Gong">Zeng Gong</a> (1019–1083)</li> <li><a href="/wiki/Sima_Guang" title="Sima Guang">Sima Guang</a> (1019–1086)</li> <li><a href="/wiki/Zhang_Zai" title="Zhang Zai">Zhang Zai</a> (1022–1077)</li> <li><a href="/wiki/Cheng_Hao" title="Cheng Hao">Cheng Hao</a> (1032–1085)</li> <li><a href="/wiki/Cheng_Yi_(philosopher)" title="Cheng Yi (philosopher)">Cheng Yi</a> (1033–1107)</li> <li><a href="/wiki/Su_Shi" title="Su Shi">Su Shi</a> (1037–1101)</li> <li><a href="/wiki/Su_Zhe" title="Su Zhe">Su Zhe</a> (1039–1112)</li> <li><a href="/wiki/Huang_Tingjian" title="Huang Tingjian">Huang Tingjian</a> (1045–1105)</li> <li><a href="/wiki/Cai_Jing" title="Cai Jing">Cai Jing</a> (1047–1126)</li> <li><a href="/wiki/Zhou_Bangyan" title="Zhou Bangyan">Zhou Bangyan</a> (1056–1121)</li> <li><a href="/wiki/Li_Qingzhao" title="Li Qingzhao">Li Qingzhao</a> (1084–1155)</li> <li><a href="/wiki/Zhu_Bian" title="Zhu Bian">Zhu Bian</a> (1085–1144)</li> <li><a href="/wiki/Zhu_Yu_(author)" title="Zhu Yu (author)">Zhu Yu</a> (<abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr><span style="white-space:nowrap;"> 1111–1117</span>)</li> <li><a href="/wiki/Lu_You" title="Lu You">Lu You</a> (1125–1209)</li> <li><a href="/wiki/Fan_Chengda" title="Fan Chengda">Fan Chengda</a> (1126–1193)</li> <li><a href="/wiki/Yang_Wanli" title="Yang Wanli">Yang Wanli</a> (1127–1206)</li> <li><a href="/wiki/Zhu_Xi" title="Zhu Xi">Zhu Xi</a> (1130–1200)</li> <li><a href="/wiki/Xin_Qiji" title="Xin Qiji">Xin Qiji</a> (1140–1207)</li> <li><a href="/wiki/Zhao_Rukuo" title="Zhao Rukuo">Zhao Rukuo</a> (1170–1231)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align: center;">Painters</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/Fan_Kuan" title="Fan Kuan">Fan Kuan</a> (960–1030)</li> <li><a href="/wiki/Xu_Daoning" title="Xu Daoning">Xu Daoning</a> (970–1053)</li> <li><a href="/wiki/Zhao_Chang" title="Zhao Chang">Zhao Chang</a> (10th c.)</li> <li><a href="/wiki/Yi_Yuanji" title="Yi Yuanji">Yi Yuanji</a> (1000–1064)</li> <li><a href="/wiki/Wen_Tong" title="Wen Tong">Wen Tong</a> (1019–1079)</li> <li><a href="/wiki/Guo_Xi" title="Guo Xi">Guo Xi</a> (1020–1090)</li> <li><a href="/wiki/Wang_Shen_(Song_dynasty)" title="Wang Shen (Song dynasty)">Wang Shen</a> (1036–1093)</li> <li><a href="/wiki/Li_Gonglin" title="Li Gonglin">Li Gonglin</a> (1049–1106)</li> <li><a href="/wiki/Cui_Bai" title="Cui Bai">Cui Bai</a> (<abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr><span style="white-space:nowrap;"> 1050–1080</span>)</li> <li><a href="/wiki/Mi_Fu" title="Mi Fu">Mi Fu</a> (1051–1107)</li> <li><a href="/wiki/Emperor_Huizong_of_Song" title="Emperor Huizong of Song">Emperor Huizong</a> (1082–1135)</li> <li><a href="/wiki/Zhang_Zeduan" title="Zhang Zeduan">Zhang Zeduan</a> (1085–1145)</li> <li><a href="/wiki/Su_Hanchen" title="Su Hanchen">Su Hanchen</a> (1094-1172)</li> <li><a href="/wiki/Wang_Ximeng" title="Wang Ximeng">Wang Ximeng</a> (1096–1119)</li> <li><a href="/wiki/Li_Di" title="Li Di">Li Di</a> (1100–1197)</li> <li><a href="/wiki/Zhao_Boju" title="Zhao Boju">Zhao Boju</a> (1120–1182)</li> <li><a href="/wiki/Liang_Kai" title="Liang Kai">Liang Kai</a> (1140–1210)</li> <li><a href="/wiki/Lin_Tinggui" title="Lin Tinggui">Lin Tinggui</a> (<abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr><span style="white-space:nowrap;"> 1174–1189</span>)</li> <li><a href="/wiki/Zhou_Jichang" title="Zhou Jichang">Zhou Jichang</a> (12th c.)</li> <li><a href="/wiki/Wuzhun_Shifan" title="Wuzhun Shifan">Wuzhun Shifan</a> (1178–1249)</li> <li><a href="/wiki/Li_Song_(painter)" title="Li Song (painter)">Li Song</a> (1190–1230)</li> <li><a href="/wiki/Zhao_Mengjian" title="Zhao Mengjian">Zhao Mengjian</a> (1199–1295)</li> <li><a href="/wiki/Muqi" title="Muqi">Muqi</a> (1210–1269)</li> <li><a href="/wiki/Gong_Kai" title="Gong Kai">Gong Kai</a> (1222–1307)</li> <li><a href="/wiki/Qian_Xuan" title="Qian Xuan">Qian Xuan</a> (1235–1305)</li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Economy_of_the_Song_dynasty" title="Economy of the Song dynasty">Economy</a></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/Wang_Anshi" title="Wang Anshi">Wang Anshi</a> (1021–1086)</li> <li><a href="/wiki/Joint-stock_company" title="Joint-stock company">Joint-stock company</a></li> <li><a href="/wiki/Banknote" title="Banknote">Banknote</a> <ul><li><a href="/wiki/Jiaozi_(currency)" title="Jiaozi (currency)">Jiaozi</a></li> <li><a href="/wiki/Guanzi_(currency)" title="Guanzi (currency)">Guanzi</a></li> <li><a href="/wiki/Huizi_(currency)" title="Huizi (currency)">Huizi</a></li></ul></li> <li><a href="/wiki/Southern_Song_dynasty_coinage" title="Southern Song dynasty coinage">Southern Song dynasty coinage</a></li> <li><a href="/wiki/Champa_rice" title="Champa rice">Champa rice</a></li> <li><a href="/wiki/Nanhai_One" title="Nanhai One">Nanhai One</a></li> <li><i><a href="/wiki/Zhu_Fan_Zhi" title="Zhu Fan Zhi">Zhu Fan Zhi</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Science_and_technology_of_the_Song_dynasty" title="Science and technology of the Song dynasty">Science and technology</a></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/Gunpowder" title="Gunpowder">Gunpowder</a> <ul><li><a href="/wiki/Gunpowder_weapons_in_the_Song_dynasty" title="Gunpowder weapons in the Song dynasty">Gunpowder weapons</a></li> <li><i><a href="/wiki/Wujing_Zongyao" title="Wujing Zongyao">Wujing Zongyao</a></i></li></ul></li> <li><a href="/wiki/Coke_(fuel)" title="Coke (fuel)">Coke</a></li> <li><a href="/wiki/Bessemer_process" title="Bessemer process">Early Bessemer process</a></li> <li><a href="/wiki/Chain_drive" title="Chain drive">Endless power transmitting chain drive</a></li> <li><a href="/wiki/Astronomical_clock" title="Astronomical clock">Astronomical clock</a></li> <li><a href="/wiki/Movable_type" title="Movable type">Movable type</a></li> <li><a href="/wiki/Compass" title="Compass">Compass</a></li> <li><a href="/wiki/Lock_(water_navigation)" title="Lock (water navigation)">Pound lock</a></li> <li><a href="/wiki/Dry_dock" title="Dry dock">Dry dock</a></li> <li><a href="/wiki/Bulkhead_(partition)" title="Bulkhead (partition)">Watertight bulkhead</a></li> <li><a href="/wiki/Fishing_reel" title="Fishing reel">Fishing reel</a></li> <li><a href="/wiki/Tianchi_basin" title="Tianchi basin">Tianchi basin</a></li> <li><a href="/wiki/Horner%27s_method" title="Horner's method">Horner's method</a></li> <li><a href="/wiki/Architecture_of_the_Song_dynasty" title="Architecture of the Song dynasty">Architecture</a> <ul><li><a href="/wiki/Liaodi_Pagoda" title="Liaodi Pagoda">Liaodi Pagoda</a></li> <li><i><a href="/wiki/Yingzao_Fashi" title="Yingzao Fashi">Yingzao Fashi</a></i></li></ul></li> <li><a href="/wiki/Forensic_entomology" title="Forensic entomology">Forensic entomology</a> <ul><li><i><a href="/wiki/Collected_Cases_of_Injustice_Rectified" title="Collected Cases of Injustice Rectified">Collected Cases of Injustice Rectified</a></i></li></ul></li> <li><i><a href="/wiki/Dream_Pool_Essays" title="Dream Pool Essays">Dream Pool Essays</a></i></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Inventors" scope="row" class="navbox-group" style="width:1%;text-align: center;">Inventors</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/Bi_Sheng" title="Bi Sheng">Bi Sheng</a> (972–1051)</li> <li><a href="/wiki/Zhang_Sixun" title="Zhang Sixun">Zhang Sixun</a> (<abbr title="floruit ('flourished' – known to have been active at a particular time or during a particular period)">fl.</abbr><span style="white-space:nowrap;"> 10th c.</span>)</li> <li><a href="/wiki/Jia_Xian" title="Jia Xian">Jia Xian</a> (1010–1070)</li> <li><a href="/wiki/Su_Song" title="Su Song">Su Song</a> (1020–1101)</li> <li><a href="/wiki/Shen_Kuo" title="Shen Kuo">Shen Kuo</a> (1031–1095)</li> <li><a href="/wiki/Song_Ci" title="Song Ci">Song Ci</a> (1186–1249)</li> <li><a class="mw-selflink selflink">Li Ye</a> (1192-1279)</li> <li><a href="/wiki/Qin_Jiushao" title="Qin Jiushao">Qin Jiushao</a> (1202–1261)</li> <li><a href="/wiki/Guo_Shoujing" title="Guo Shoujing">Guo Shoujing</a> (1231–1316)</li></ul> </div></td></tr></tbody></table><div> </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" 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