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mw-first-heading"><span class="mw-page-title-main">Azimuthal equidistant projection</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 11 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-11" 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">11 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Projecci%C3%B3_azimutal_equidistant" title="Projecció azimutal equidistant – Catalan" lang="ca" hreflang="ca" data-title="Projecció azimutal equidistant" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mittabstandstreue_Azimutalprojektion" title="Mittabstandstreue Azimutalprojektion – German" lang="de" hreflang="de" data-title="Mittabstandstreue Azimutalprojektion" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Proyecci%C3%B3n_acimutal_equidistante" title="Proyección acimutal equidistante – Spanish" lang="es" hreflang="es" data-title="Proyección acimutal equidistante" 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/Projection_de_Postel" title="Projection de Postel – French" lang="fr" hreflang="fr" data-title="Projection de Postel" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%95%EA%B1%B0_%EB%B0%A9%EC%9C%84_%EB%8F%84%EB%B2%95" title="정거 방위 도법 – Korean" lang="ko" hreflang="ko" data-title="정거 방위 도법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Proiezione_azimutale_equidistante" title="Proiezione azimutale equidistante – Italian" lang="it" hreflang="it" data-title="Proiezione azimutale equidistante" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Afstandsgetrouwe_azimutale_projectie" title="Afstandsgetrouwe azimutale projectie – Dutch" lang="nl" hreflang="nl" data-title="Afstandsgetrouwe azimutale projectie" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%AD%A3%E8%B7%9D%E6%96%B9%E4%BD%8D%E5%9B%B3%E6%B3%95" title="正距方位図法 – Japanese" lang="ja" hreflang="ja" data-title="正距方位図法" 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Odwzorowanie_azymutalne_r%C3%B3wnoodleg%C5%82o%C5%9Bciowe" title="Odwzorowanie azymutalne równoodległościowe – Polish" lang="pl" hreflang="pl" data-title="Odwzorowanie azymutalne równoodległościowe" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></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">Azimuthal equidistant map projection</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Azimuthal_equidistant_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Azimuthal_equidistant_projection_SW.jpg/300px-Azimuthal_equidistant_projection_SW.jpg" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Azimuthal_equidistant_projection_SW.jpg/450px-Azimuthal_equidistant_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Azimuthal_equidistant_projection_SW.jpg/600px-Azimuthal_equidistant_projection_SW.jpg 2x" data-file-width="2058" data-file-height="2058" /></a><figcaption>An azimuthal equidistant projection about the <a href="/wiki/North_Pole" title="North Pole">North Pole</a> extending all the way to the <a href="/wiki/South_Pole" title="South Pole">South Pole</a></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Azimuthal_equidistant_projection_south_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Azimuthal_equidistant_projection_south_SW.jpg/300px-Azimuthal_equidistant_projection_south_SW.jpg" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Azimuthal_equidistant_projection_south_SW.jpg/450px-Azimuthal_equidistant_projection_south_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Azimuthal_equidistant_projection_south_SW.jpg/600px-Azimuthal_equidistant_projection_south_SW.jpg 2x" data-file-width="2058" data-file-height="2058" /></a><figcaption>An azimuthal equidistant projection about the <a href="/wiki/South_Pole" title="South Pole">South Pole</a> extending all the way to the <a href="/wiki/North_Pole" title="North Pole">North Pole</a></figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Emblem_of_the_United_Nations.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Emblem_of_the_United_Nations.svg/300px-Emblem_of_the_United_Nations.svg.png" decoding="async" width="300" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Emblem_of_the_United_Nations.svg/450px-Emblem_of_the_United_Nations.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Emblem_of_the_United_Nations.svg/600px-Emblem_of_the_United_Nations.svg.png 2x" data-file-width="512" data-file-height="436" /></a><figcaption>Emblem of the <a href="/wiki/United_Nations" title="United Nations">United Nations</a> containing a polar azimuthal equidistant projection</figcaption></figure> <p>The <b>azimuthal equidistant projection</b> is an <a href="/wiki/Azimuthal_projection#Azimuthal_.28projections_onto_a_plane.29" class="mw-redirect" title="Azimuthal projection">azimuthal map projection</a>. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct <a href="/wiki/Azimuth" title="Azimuth">azimuth</a> (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. </p><p>The <a href="/wiki/United_Nations_flag" class="mw-redirect" title="United Nations flag">flag of the United Nations</a> contains an example of a polar azimuthal equidistant projection. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuthal_equidistant_projection&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>While it may have been used by <a href="/wiki/Ancient_Egypt" title="Ancient Egypt">ancient Egyptians</a> for star maps in some holy books,<sup id="cite_ref-Snyder_1-0" class="reference"><a href="#cite_note-Snyder-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> the earliest text describing the azimuthal equidistant projection is an 11th-century work by <a href="/wiki/Abu_Rayhan_Biruni" class="mw-redirect" title="Abu Rayhan Biruni">al-Biruni</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> </p><p>An example of this system is the world map by ‛Ali b. Ahmad al-Sharafi of Sfax in 1571.<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> </p><p>The projection appears in many Renaissance maps, and <a href="/wiki/Gerardus_Mercator" title="Gerardus Mercator">Gerardus Mercator</a> used it for an inset of the north polar regions in sheet 13 and legend 6 of his well-known <a href="/wiki/Mercator_1569_world_map" title="Mercator 1569 world map">1569 map</a>. In France and Russia this projection is named "Postel projection" after <a href="/wiki/Guillaume_Postel" title="Guillaume Postel">Guillaume Postel</a>, who used it for a map in 1581.<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> Many modern star chart <a href="/wiki/Planisphere" title="Planisphere">planispheres</a> use the polar azimuthal equidistant projection. </p> <div class="thumb tnone" style="margin-left:auto;margin-right:auto;overflow:hidden;width:auto;max-width:776px"><div class="thumbinner"><div class="noresize" style="overflow:auto"><span typeof="mw:File"><a href="/wiki/File:Comparison_azimuthal_projections.svg" class="mw-file-description" title="Comparison of the Azimuthal equidistant projection and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii. (click for detail)"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/768px-Comparison_azimuthal_projections.svg.png" decoding="async" width="768" height="257" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/1152px-Comparison_azimuthal_projections.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Comparison_azimuthal_projections.svg/1536px-Comparison_azimuthal_projections.svg.png 2x" data-file-width="512" data-file-height="171" /></a></span></div><div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Comparison_azimuthal_projections.svg" title="File:Comparison azimuthal projections.svg"> </a></div>Comparison of the <i>Azimuthal equidistant projection</i> and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii. <a class="external text" href="https://upload.wikimedia.org/wikipedia/commons/b/ba/Comparison_azimuthal_projections.svg">(click for detail)</a></div></div></div> <p><br /> The polar azimuthal equidistant projection has also been adopted by <a href="/wiki/Modern_flat_Earth_beliefs" title="Modern flat Earth beliefs">21st century Flat Earthers</a> as a map of the Flat Earth, particularly due to its use in the UN flag and its depiction of Antarctica as a ring around the edge of the Earth.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Mathematical_definition">Mathematical definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuthal_equidistant_projection&action=edit&section=2" title="Edit section: Mathematical definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png" class="mw-file-description"><img alt="Tissot's indicatrix applied to the azimuthal equidistant projection" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png/124px-Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png" decoding="async" width="124" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png/186px-Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png/248px-Azimuthal_equidistant_projection_with_Tissot%27s_indicatrix.png 2x" data-file-width="680" data-file-height="680" /></a><figcaption> <a href="/wiki/Tissot%27s_indicatrix" title="Tissot's indicatrix">Tissot's indicatrix</a> applied to the azimuthal equidistant projection</figcaption></figure> <p>A point on the globe is chosen as "the center" in the sense that mapped distances and <a href="/wiki/Azimuth" title="Azimuth">azimuth</a> directions from that point to any other point will be correct. That point, (<i>φ</i><sub>0</sub>, <i>λ</i><sub>0</sub>), will project to the center of a circular projection, with <i>φ</i> referring to latitude and <i>λ</i> referring to longitude. All points along a given azimuth will project along a straight line from the center, and the angle <i>θ</i> that the line subtends from the vertical is the azimuth angle. The distance from the center point to another projected point <i>ρ</i> is the <a href="/wiki/Arc_length" title="Arc length">arc length</a> along a <a href="/wiki/Great_circle" title="Great circle">great circle</a> between them on the globe. By this description, then, the point on the plane specified by (<i>θ</i>,<i>ρ</i>) will be projected to Cartesian coordinates: </p> <dl><dd><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 x=\rho \sin \theta ,\qquad y=-\rho \cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>ρ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mo>,</mo> <mspace width="2em" /> <mi>y</mi> <mo>=</mo> <mo>−</mo> <mi>ρ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=\rho \sin \theta ,\qquad y=-\rho \cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66d6dae2afbae1245eccd4a8fc324ecfa3d512a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.269ex; height:2.676ex;" alt="{\displaystyle x=\rho \sin \theta ,\qquad y=-\rho \cos \theta }"></span></dd></dl> <p>The relationship between the coordinates (<i>θ</i>,<i>ρ</i>) of the point on the globe, and its latitude and longitude coordinates (<i>φ</i>, <i>λ</i>) is given by the equations: <sup id="cite_ref-Album_6-0" class="reference"><a href="#cite_note-Album-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 {\begin{aligned}\cos {\frac {\rho }{R}}&=\sin \varphi _{0}\sin \varphi +\cos \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)\\\tan \theta &={\frac {\cos \varphi \sin \left(\lambda -\lambda _{0}\right)}{\cos \varphi _{0}\sin \varphi -\sin \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ρ</mi> <mi>R</mi> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>λ</mi> <mo>−</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>tan</mi> <mo>⁡</mo> <mi>θ</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>λ</mi> <mo>−</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi>λ</mi> <mo>−</mo> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\cos {\frac {\rho }{R}}&=\sin \varphi _{0}\sin \varphi +\cos \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)\\\tan \theta &={\frac {\cos \varphi \sin \left(\lambda -\lambda _{0}\right)}{\cos \varphi _{0}\sin \varphi -\sin \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d3220eca224e6678f968f8b5a0186720d561ebb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.171ex; width:47.982ex; height:11.509ex;" alt="{\displaystyle {\begin{aligned}\cos {\frac {\rho }{R}}&=\sin \varphi _{0}\sin \varphi +\cos \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)\\\tan \theta &={\frac {\cos \varphi \sin \left(\lambda -\lambda _{0}\right)}{\cos \varphi _{0}\sin \varphi -\sin \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)}}\end{aligned}}}"></span></dd></dl> <p>When the center point is the north pole, <i>φ</i><sub>0</sub> equals <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 /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \pi /2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b44e3d874a0b229fded7ffce67a0677dd5b8b67" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.657ex; height:2.843ex;" alt="{\displaystyle \pi /2}"></span> and <i>λ</i><sub>0</sub> is arbitrary, so it is most convenient to assign it the value of 0. This assignment significantly simplifies the equations for <i>ρ</i><sub>u</sub> and <i>θ</i> to: </p> <dl><dd><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 \rho =R\left({\frac {\pi }{2}}-\varphi \right),\qquad \theta =\lambda ~~}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mo>=</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> <mo>−</mo> <mi>φ</mi> </mrow> <mo>)</mo> </mrow> <mo>,</mo> <mspace width="2em" /> <mi>θ</mi> <mo>=</mo> <mi>λ</mi> <mtext> </mtext> <mtext> </mtext> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho =R\left({\frac {\pi }{2}}-\varphi \right),\qquad \theta =\lambda ~~}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3961ad081c8cc44ae8503337d455fce7959066f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:28.527ex; height:4.843ex;" alt="{\displaystyle \rho =R\left({\frac {\pi }{2}}-\varphi \right),\qquad \theta =\lambda ~~}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Limitation">Limitation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuthal_equidistant_projection&action=edit&section=3" title="Edit section: Limitation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>With the <a href="/wiki/Earth%27s_circumference" title="Earth's circumference">circumference of the Earth</a> being approximately 40,000 km (24,855 mi), the maximum distance that can be displayed on an azimuthal equidistant projection map is half the circumference, or about 20,000 km (12,427 mi). For distances less than 10,000 km (6,214 mi) distortions are minimal. For distances 10,000–15,000 km (6,214–9,321 mi) the distortions are moderate. Distances greater than 15,000 km (9,321 mi) are severely distorted. </p><p>If the azimuthal equidistant projection map is centered about a point whose <a href="/wiki/Antipodes" title="Antipodes">antipodal point</a> lies on land and the map is extended to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle. This is shown in the example of two maps centered about <a href="/wiki/Los_Angeles" title="Los Angeles">Los Angeles</a>, and <a href="/wiki/Taipei" title="Taipei">Taipei</a>. The antipode for Los Angeles is in the south <a href="/wiki/Indian_Ocean" title="Indian Ocean">Indian Ocean</a> hence there is not much significant distortion of land masses for the Los Angeles centered map except for <a href="/wiki/East_Africa" title="East Africa">East Africa</a> and <a href="/wiki/Madagascar" title="Madagascar">Madagascar</a>. On the other hand, Taipei's antipode is near the <a href="/wiki/Argentina%E2%80%93Paraguay_border" title="Argentina–Paraguay border">Argentina–Paraguay border</a>, causing the Taipei centered map to severely distort <a href="/wiki/South_America" title="South America">South America</a>. </p> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:528px;max-width:528px"><div class="trow"><div class="theader" style="text-align:center">Sample azimuthal equidistant projection maps</div></div><div class="trow"><div class="tsingle" style="width:262px;max-width:262px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Los_Angeles_centered_azimuthal_equidistant_projection.gif" class="mw-file-description"><img alt="An azimuthal equidistant projection centered about Los Angeles." src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Los_Angeles_centered_azimuthal_equidistant_projection.gif/260px-Los_Angeles_centered_azimuthal_equidistant_projection.gif" decoding="async" width="260" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Los_Angeles_centered_azimuthal_equidistant_projection.gif/390px-Los_Angeles_centered_azimuthal_equidistant_projection.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Los_Angeles_centered_azimuthal_equidistant_projection.gif/520px-Los_Angeles_centered_azimuthal_equidistant_projection.gif 2x" data-file-width="4000" data-file-height="4000" /></a></span></div><div class="thumbcaption">Map centered about <a href="/wiki/Los_Angeles" title="Los Angeles">Los Angeles</a>, whose <a href="/wiki/Antipodes" title="Antipodes">antipodal point</a> is in the south <a href="/wiki/Indian_Ocean" title="Indian Ocean">Indian Ocean</a><br /><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:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#21B04B; color:#21B04B;">    </span> <a href="/wiki/California" title="California">California</a></span></li></ul></div></div></div><div class="tsingle" style="width:262px;max-width:262px"><div class="thumbimage"><span typeof="mw:File"><a href="/wiki/File:Taipei_centered_azimuthal_equidistant_projection.gif" class="mw-file-description"><img alt="An azimuthal equidistant projection centered about Taipei." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Taipei_centered_azimuthal_equidistant_projection.gif/260px-Taipei_centered_azimuthal_equidistant_projection.gif" decoding="async" width="260" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Taipei_centered_azimuthal_equidistant_projection.gif/390px-Taipei_centered_azimuthal_equidistant_projection.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Taipei_centered_azimuthal_equidistant_projection.gif/520px-Taipei_centered_azimuthal_equidistant_projection.gif 2x" data-file-width="4000" data-file-height="4000" /></a></span></div><div class="thumbcaption">Map centered about <a href="/wiki/Taipei" title="Taipei">Taipei</a>, whose <a href="/wiki/Antipodes" title="Antipodes">antipodal point</a> is near the <a href="/wiki/Argentina%E2%80%93Paraguay_border" title="Argentina–Paraguay border">Argentina–Paraguay border</a><br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist"><ul><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#21B04B; color:#21B04B;">    </span> <a href="/wiki/Taiwan" title="Taiwan">Taiwan</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#FFFF00; color:#FFFF00;">    </span> <a href="/wiki/Brazil" title="Brazil">Brazil</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#FFA500; color:#FFA500;">    </span> <a href="/wiki/Paraguay" title="Paraguay">Paraguay</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#FFC0CB; color:#FFC0CB;">    </span> <a href="/wiki/Argentina" title="Argentina">Argentina</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#ADFF2F; color:#ADFF2F;">    </span> <a href="/wiki/Chile" title="Chile">Chile</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#DDA0DD; color:#DDA0DD;">    </span> <a href="/wiki/Bolivia" title="Bolivia">Bolivia</a></span></li><li><span style="margin:0px; font-size:90%;"><span style="border:none; background-color:#DCDCDC; color:#DCDCDC;">    </span> <a href="/wiki/Uruguay" title="Uruguay">Uruguay</a></span></li></ul></div></div></div></div><div class="trow" style="display:flow-root"><div class="thumbcaption" style="text-align:center"><style data-mw-deduplicate="TemplateStyles:r981673959">.mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}</style><div class="legend"><span class="legend-line mw-no-invert" style="display: inline-block; vertical-align: middle; width: 1.67em; height: 0; border-style: none; border-top: 2px dotted black;border-top:red solid 2px;"> </span> Red circles: 10,000 km radius circles</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r981673959"><div class="legend"><span class="legend-line mw-no-invert" style="display: inline-block; vertical-align: middle; width: 1.67em; height: 0; border-style: none; border-top: 2px dotted black;border-top:purple solid 2px;"> </span> Purple circles: 15,000 km radius circles</div></div></div></div></div> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Azimuthal_equidistant_projection&action=edit&section=4" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Gcmsyd.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Gcmsyd.jpg/250px-Gcmsyd.jpg" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Gcmsyd.jpg/375px-Gcmsyd.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Gcmsyd.jpg/500px-Gcmsyd.jpg 2x" data-file-width="700" data-file-height="700" /></a><figcaption>An azimuthal equidistant projection centered on Sydney</figcaption></figure> <p>Azimuthal equidistant projection maps can be useful in terrestrial <a href="/wiki/Point_to_point_communication" class="mw-redirect" title="Point to point communication">point to point communication</a>. This type of projection allows the operator to easily determine in which direction to point their <a href="/wiki/Directional_antenna" title="Directional antenna">directional antenna</a>. The operator simply finds on the map the location of the target transmitter or receiver (i.e. the other antenna being communicated with) and uses the map to determine the <a href="/wiki/Azimuth" title="Azimuth">azimuth angle</a> needed to point the operator's antenna. The operator would use an <a href="/wiki/Antenna_rotator" title="Antenna rotator">electric rotator</a> to point the antenna. The map can also be used in one way communication. For example if the operator is looking to receive signals from a distant radio station, this type of projection could help identify the direction of the distant radio station. In order for the map to be useful, the map should be centered as close as possible about the location of the operator's antenna.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (October 2016)">citation needed</span></a></i>]</sup> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:North_Korean_missile_range.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/North_Korean_missile_range.svg/250px-North_Korean_missile_range.svg.png" decoding="async" width="250" height="250" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/32/North_Korean_missile_range.svg/375px-North_Korean_missile_range.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/32/North_Korean_missile_range.svg/500px-North_Korean_missile_range.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>An azimuthal equidistant projection centered on North Korea along with ranges of <a href="/wiki/List_of_North_Korean_missile_tests" title="List of North Korean missile tests">their different missiles</a></figcaption></figure> <p>Azimuthal equidistant projection maps can also be useful to show ranges of ballistic missiles, as demonstrated by the map centered on North Korea showing the country's missile range. </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=Azimuthal_equidistant_projection&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert azimuthal equal-area projection</a></li> <li><a href="/wiki/List_of_map_projections" title="List of map projections">List of map projections</a></li> <li><a href="/wiki/Modern_flat_Earth_beliefs" title="Modern flat Earth beliefs">Modern flat Earth beliefs</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=Azimuthal_equidistant_projection&action=edit&section=6" 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"><ol class="references"> <li id="cite_note-Snyder-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Snyder_1-0">^</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="CITEREFSNYDER1997" class="citation book cs1">SNYDER, John P. (1997). <i>Flattening the earth: two thousand years of map projections</i>. University of Chicago Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-226-76747-7" title="Special:BookSources/0-226-76747-7"><bdi>0-226-76747-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Flattening+the+earth%3A+two+thousand+years+of+map+projections&rft.pub=University+of+Chicago+Press&rft.date=1997&rft.isbn=0-226-76747-7&rft.aulast=SNYDER&rft.aufirst=John+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuthal+equidistant+projection" class="Z3988"></span>, p.29</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">David A. KING (1996), "Astronomy and Islamic society: Qibla, gnomics and timekeeping", in Roshdi Rashed, ed., <i><a href="/wiki/Encyclopedia_of_the_History_of_Arabic_Science" title="Encyclopedia of the History of Arabic Science">Encyclopedia of the History of Arabic Science</a></i>, Vol. 1, p. 128–184 [153]. <a href="/wiki/Routledge" title="Routledge">Routledge</a>, London and New York.</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"> Edward S. Kennedy, 1996, Mathematical geography, in Roshdi Rashed, ed., <i><a href="/wiki/Encyclopedia_of_the_History_of_Arabic_Science" title="Encyclopedia of the History of Arabic Science">Encyclopedia of the History of Arabic Science</a></i>, Vol. 1, <a href="/wiki/Routledge" title="Routledge">Routledge</a>, London and New York.</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">Snyder 1997, p. 29</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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://leadstories.com/hoax-alert/2022/09/fact-check-the-un-flag-does-not-show-flat-earth.html">"Fact Check: The UN Flag Does NOT Show Flat Earth | Lead Stories"</a>. <i>leadstories.com</i>. 2022-09-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2024-02-04</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=leadstories.com&rft.atitle=Fact+Check%3A+The+UN+Flag+Does+NOT+Show+Flat+Earth+%7C+Lead+Stories&rft.date=2022-09-12&rft_id=https%3A%2F%2Fleadstories.com%2Fhoax-alert%2F2022%2F09%2Ffact-check-the-un-flag-does-not-show-flat-earth.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuthal+equidistant+projection" class="Z3988"></span></span> </li> <li id="cite_note-Album-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Album_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSnyderVoxland1989" class="citation book cs1"><a href="/wiki/John_P._Snyder" title="John P. Snyder">Snyder, John P.</a>; <a href="/w/index.php?title=Philip_M._Voxland&action=edit&redlink=1" class="new" title="Philip M. Voxland (page does not exist)">Voxland, Philip M.</a> (1989). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100701102858/http://pubs.er.usgs.gov/usgspubs/pp/pp1453"><i>An Album of Map Projections</i></a>. Professional Paper 1453. Denver: <a href="/wiki/United_States_Geological_Survey" title="United States Geological Survey">USGS</a>. p. 228. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0160033681" title="Special:BookSources/978-0160033681"><bdi>978-0160033681</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://pubs.er.usgs.gov/usgspubs/pp/pp1453">the original</a> on 2010-07-01<span class="reference-accessdate">. Retrieved <span class="nowrap">2018-03-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=An+Album+of+Map+Projections&rft.place=Denver&rft.series=Professional+Paper+1453&rft.pages=228&rft.pub=USGS&rft.date=1989&rft.isbn=978-0160033681&rft.aulast=Snyder&rft.aufirst=John+P.&rft.au=Voxland%2C+Philip+M.&rft_id=https%3A%2F%2Fpubs.er.usgs.gov%2Fusgspubs%2Fpp%2Fpp1453&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAzimuthal+equidistant+projection" class="Z3988"></span></span> </li> </ol></div></div> <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=Azimuthal_equidistant_projection&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.radicalcartography.net/?projectionref">Table of examples and properties of all common projections</a>, from radicalcartography.net</li> <li><a rel="nofollow" class="external text" href="http://www.wm7d.net/azproj.shtml">Online Azimuthal Equidistant Map Generator</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070927225345/http://www.uff.br/mapprojections/AzimuthalEquidistant_en.html">An interactive Java Applet to study the metric deformations of the Azimuthal Equidistant Projection</a>.</li> <li><a rel="nofollow" class="external text" href="https://geographiclib.sourceforge.io">GeographicLib</a> provides a class for performing azimuthal equidistant projections centered at any point on the ellipsoid.</li> <li><a rel="nofollow" class="external text" href="http://earth.nullschool.net/#current/wind/isobaric/500hPa/azimuthal_equidistant=24.64,98.15,169">Animated US National Weather Service Wind Data for Azimuthal equidistant projection</a>.</li> <li><a rel="nofollow" class="external text" href="https://ns6t.net/azimuth/azimuth.html">Generate an Azimuthal equidistant projection from any point on Earth</a> from ns6t.net.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output 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.navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Map_projections" title="Template:Map projections"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Map_projections" title="Template talk:Map projections"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Map_projections" title="Special:EditPage/Template:Map projections"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Map_projection" style="font-size:114%;margin:0 4em"><a href="/wiki/Map_projection" title="Map projection">Map projection</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_cartography" title="History of cartography">History</a></li> <li><a href="/wiki/List_of_map_projections" title="List of map projections">List</a></li> <li><a href="/wiki/Portal:Maps" title="Portal:Maps">Portal</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_surface" style="font-size:114%;margin:0 4em"><a href="/wiki/Map_projection#Projections_by_surface" title="Map projection">By surface</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" 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%"><a href="/wiki/Map_projection#Cylindrical" title="Map projection">Cylindrical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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%;font-weight: normal;"><a href="/wiki/Mercator_projection" title="Mercator projection">Mercator</a>-conformal</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/Gauss%E2%80%93Kr%C3%BCger_coordinate_system" class="mw-redirect" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li> <li><a href="/wiki/Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li> <li><a href="/wiki/Oblique_Mercator_projection" title="Oblique Mercator projection">Oblique Mercator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Equal-area</a></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/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li> <li><a href="/wiki/Behrmann_projection" title="Behrmann projection">Behrmann</a></li> <li><a href="/wiki/Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li> <li><a href="/wiki/Hobo%E2%80%93Dyer_projection" title="Hobo–Dyer projection">Hobo–Dyer</a></li> <li><a href="/wiki/Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert</a></li> <li><a href="/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li> <li><a href="/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Cassini_projection" title="Cassini projection">Cassini</a></li> <li><a href="/wiki/Central_cylindrical_projection" title="Central cylindrical projection">Central</a></li> <li><a href="/wiki/Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li> <li><a href="/wiki/Gall_stereographic_projection" title="Gall stereographic projection">Gall stereographic</a></li> <li><a href="/wiki/Gall_isographic_projection" title="Gall isographic projection">Gall isographic</a></li> <li><a href="/wiki/Miller_cylindrical_projection" title="Miller cylindrical projection">Miller</a></li> <li><a href="/wiki/Space-oblique_Mercator_projection" title="Space-oblique Mercator projection">Space-oblique Mercator</a></li> <li><a href="/wiki/Web_Mercator_projection" title="Web Mercator projection">Web Mercator</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Pseudocylindrical" title="Map projection">Pseudocylindrical</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Equal-area" scope="row" class="navbox-group" style="width:1%">Equal-area</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/Collignon_projection" title="Collignon projection">Collignon</a></li> <li><a href="/wiki/Eckert_II_projection" title="Eckert II projection">Eckert II</a></li> <li><a href="/wiki/Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li> <li><a href="/wiki/Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li> <li><a href="/wiki/Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li> <li><a href="/wiki/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li> <li><a href="/wiki/Mollweide_projection" title="Mollweide projection">Mollweide</a></li> <li><a href="/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li> <li><a href="/wiki/Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li> <li><a href="/wiki/Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li> <li><a href="/wiki/Winkel_projection" title="Winkel projection">Winkel I and II</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Conical" title="Map projection">Conical</a></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/Albers_projection" title="Albers projection">Albers</a></li> <li><a href="/wiki/Equidistant_conic_projection" title="Equidistant conic projection">Equidistant</a></li> <li><a href="/wiki/Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Pseudoconical" title="Map projection">Pseudoconical</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/Bonne_projection" title="Bonne projection">Bonne</a></li> <li><a href="/wiki/Bottomley_projection" title="Bottomley projection">Bottomley</a></li> <li><a href="/wiki/Polyconic_projection_class" title="Polyconic projection class">Polyconic</a> <ul><li><a href="/wiki/American_polyconic_projection" title="American polyconic projection">American</a></li> <li><a href="/wiki/Latitudinally_equal-differential_polyconic_projection" title="Latitudinally equal-differential polyconic projection">Chinese</a></li></ul></li> <li><a href="/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Azimuthal" title="Map projection">Azimuthal<br /><span class="nobold">(planar)</span></a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="General_perspective" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/General_Perspective_projection" title="General Perspective projection">General perspective</a></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/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li> <li><a href="/wiki/Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li> <li><a href="/wiki/Stereographic_map_projection" title="Stereographic map projection">Stereographic</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Equidistant</a></li> <li><a href="/wiki/Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert equal-area</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Pseudoazimuthal" title="Map projection">Pseudoazimuthal</a></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/Aitoff_projection" title="Aitoff projection">Aitoff</a></li> <li><a href="/wiki/Hammer_projection" title="Hammer projection">Hammer</a></li> <li><a href="/wiki/Wiechel_projection" title="Wiechel projection">Wiechel</a></li> <li><a href="/wiki/Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_metric" style="font-size:114%;margin:0 4em"><a href="/wiki/Map_projection#Projections_by_preservation_of_a_metric_property" title="Map projection">By metric</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" 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%"><a href="/wiki/Conformal_map_projection" title="Conformal map projection">Conformal</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/Adams_hemisphere-in-a-square_projection" title="Adams hemisphere-in-a-square projection">Adams hemisphere-in-a-square</a></li> <li><a href="/wiki/Gauss%E2%80%93Kr%C3%BCger_coordinate_system" class="mw-redirect" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li> <li><a href="/wiki/Guyou_hemisphere-in-a-square_projection" title="Guyou hemisphere-in-a-square projection">Guyou hemisphere-in-a-square</a></li> <li><a href="/wiki/Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal conic</a></li> <li><a href="/wiki/Mercator_projection" title="Mercator projection">Mercator</a></li> <li><a href="/wiki/Peirce_quincuncial_projection" title="Peirce quincuncial projection">Peirce quincuncial</a></li> <li><a href="/wiki/Stereographic_projection" title="Stereographic projection">Stereographic</a></li> <li><a href="/wiki/Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Equal-area_projection" title="Equal-area projection">Equal-area</a></th><td class="navbox-list-with-group navbox-list navbox-odd" 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%;font-weight: normal;"><a href="/wiki/Bonne_projection" title="Bonne projection">Bonne</a></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/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li> <li><a href="/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/Bottomley_projection" title="Bottomley projection">Bottomley</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/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li> <li><a href="/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Cylindrical</a></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/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li> <li><a href="/wiki/Behrmann_projection" title="Behrmann projection">Behrmann</a></li> <li><a href="/wiki/Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li> <li><a href="/wiki/Hobo%E2%80%93Dyer_projection" title="Hobo–Dyer projection">Hobo–Dyer</a></li> <li><a href="/wiki/Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert cylindrical equal-area</a></li> <li><a href="/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li> <li><a href="/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</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/Collignon_projection" title="Collignon projection">Collignon</a></li> <li><a href="/wiki/Mollweide_projection" title="Mollweide projection">Mollweide</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Albers_projection" title="Albers projection">Albers</a></li> <li><a href="/wiki/Hammer_projection#Briesemeister" title="Hammer projection">Briesemeister</a></li> <li><a href="/wiki/Eckert_II_projection" title="Eckert II projection">Eckert II</a></li> <li><a href="/wiki/Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li> <li><a href="/wiki/Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li> <li><a href="/wiki/Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li> <li><a href="/wiki/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li> <li><a href="/wiki/Hammer_projection" title="Hammer projection">Hammer</a></li> <li><a href="/wiki/Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert azimuthal equal-area</a></li> <li><a href="/wiki/Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li> <li><a href="/wiki/Strebe_1995_projection" title="Strebe 1995 projection">Strebe 1995</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Equidistant" title="Map projection">Equidistant in<br />some aspect</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/Equidistant_conic_projection" title="Equidistant conic projection">Conic</a></li> <li><a href="/wiki/Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li> <li><a href="/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li> <li><a href="/wiki/Two-point_equidistant_projection" title="Two-point equidistant projection">Two-point</a></li> <li><a href="/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Gnomonic" title="Map projection">Gnomonic</a></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/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Rhumb_line" title="Map projection">Loxodromic</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/Loximuthal_projection" title="Loximuthal projection">Loximuthal</a></li> <li><a href="/wiki/Mercator_projection" title="Mercator projection">Mercator</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Retroazimuthal" title="Map projection">Retroazimuthal</a><br /><span class="nobold">(Mecca or Qibla)</span></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/Craig_retroazimuthal_projection" title="Craig retroazimuthal projection">Craig</a></li> <li><a href="/wiki/Hammer_retroazimuthal_projection" title="Hammer retroazimuthal projection">Hammer</a></li> <li><a href="/wiki/Littrow_projection" title="Littrow projection">Littrow</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_construction" style="font-size:114%;margin:0 4em"><a href="/wiki/Map_projection#Classification" title="Map projection">By construction</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" 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%"><a href="/wiki/Map_projection#Compromise_projections" title="Map projection">Compromise</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/Chamberlin_trimetric_projection" title="Chamberlin trimetric projection">Chamberlin trimetric</a></li> <li><a href="/wiki/Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li> <li><a href="/wiki/Miller_cylindrical_projection" title="Miller cylindrical projection">Miller cylindrical</a></li> <li><a href="/wiki/Natural_Earth_projection" title="Natural Earth projection">Natural Earth</a></li> <li><a href="/wiki/Robinson_projection" title="Robinson projection">Robinson</a></li> <li><a href="/wiki/Van_der_Grinten_projection" title="Van der Grinten projection">Van der Grinten</a></li> <li><a href="/wiki/Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li> <li><a href="/wiki/Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Hybrid" title="Map projection">Hybrid</a></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/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li> <li><a href="/wiki/HEALPix" title="HEALPix">HEALPix</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Perspective_projections" title="Map projection">Perspective</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Planar" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/wiki/General_Perspective_projection" title="General Perspective projection">Planar</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/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li> <li><a href="/wiki/Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li> <li><a href="/wiki/Stereographic_projection" title="Stereographic projection">Stereographic</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Central_cylindrical_projection" title="Central cylindrical projection">Central cylindrical</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_projection#Polyhedral" title="Map projection">Polyhedral</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/AuthaGraph_projection" title="AuthaGraph projection">AuthaGraph</a></li> <li><a href="/wiki/Bernard_J._S._Cahill" title="Bernard J. S. Cahill">Cahill Butterfly</a></li> <li><a href="/wiki/Cahill%E2%80%93Keyes_projection" title="Cahill–Keyes projection">Cahill–Keyes M-shape</a></li> <li><a href="/wiki/Dymaxion_map" title="Dymaxion map">Dymaxion</a></li> <li><a href="/wiki/Snyder_equal-area_projection" title="Snyder equal-area projection">ISEA</a></li> <li><a href="/wiki/Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li> <li><a href="/wiki/Waterman_butterfly_projection" title="Waterman butterfly projection">Waterman butterfly</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="See_also" style="font-size:114%;margin:0 4em">See also</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interruption_(map_projection)" title="Interruption (map projection)">Interruption (map projection)</a></li> <li><a href="/wiki/Latitude" title="Latitude">Latitude</a></li> <li><a href="/wiki/Longitude" title="Longitude">Longitude</a></li> <li><a href="/wiki/Tissot%27s_indicatrix" title="Tissot's indicatrix">Tissot's indicatrix</a></li> <li><a href="/wiki/Map_projection_of_the_tri-axial_ellipsoid" class="mw-redirect" title="Map projection of the tri-axial ellipsoid">Map projection of the tri-axial ellipsoid</a></li></ul> </div></td></tr></tbody></table><div></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 authority-control" aria-label="Navbox" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q1753196#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></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://id.loc.gov/authorities/sh85010650">United States</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=987007282315705171">Israel</a></span></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; 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