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For the mathematical concept, see <a href="/wiki/Measure-preserving_dynamical_system" title="Measure-preserving dynamical system">Measure-preserving dynamical system</a>.</div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Mollweide_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Mollweide_projection_SW.jpg/300px-Mollweide_projection_SW.jpg" decoding="async" width="300" height="151" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Mollweide_projection_SW.jpg/450px-Mollweide_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Mollweide_projection_SW.jpg/600px-Mollweide_projection_SW.jpg 2x" data-file-width="2058" data-file-height="1036" /></a><figcaption>The equal-area <a href="/wiki/Mollweide_projection" title="Mollweide projection">Mollweide projection</a></figcaption></figure> <p>In <a href="/wiki/Cartography" title="Cartography">cartography</a>, an <b>equivalent</b>, <b>authalic</b>, or <b>equal-area projection</b> is a <a href="/wiki/Map_projection" title="Map projection">map projection</a> that preserves relative <a href="/wiki/Area" title="Area">area</a> measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, and so forth, because an equal-area map does not change apparent density of the phenomenon being mapped. </p><p>By <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss's</a> <a href="/wiki/Theorema_Egregium" title="Theorema Egregium">Theorema Egregium</a>, an equal-area projection cannot be <a href="/wiki/Conformal_map_projection" title="Conformal map projection">conformal</a>. This implies that an equal-area projection inevitably distorts shapes. Even though a point or points or a path or paths on a map might have no distortion, the greater the area of the region being mapped, the greater and more obvious the distortion of shapes inevitably becomes. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Lambert_azimuthal_equal-area_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Lambert_azimuthal_equal-area_projection_SW.jpg/300px-Lambert_azimuthal_equal-area_projection_SW.jpg" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Lambert_azimuthal_equal-area_projection_SW.jpg/450px-Lambert_azimuthal_equal-area_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Lambert_azimuthal_equal-area_projection_SW.jpg/600px-Lambert_azimuthal_equal-area_projection_SW.jpg 2x" data-file-width="2058" data-file-height="2058" /></a><figcaption>Lambert azimuthal equal-area projection of the world centered on 0° N 0° E.</figcaption></figure> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Description">Description</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equal-area_projection&action=edit&section=1" title="Edit section: Description"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In order for a map projection of the sphere to be equal-area, its generating formulae must meet this <a href="/wiki/Cauchy-Riemann_equations" class="mw-redirect" title="Cauchy-Riemann equations">Cauchy-Riemann</a>-like condition:<sup id="cite_ref-Snyder1987_1-0" class="reference"><a href="#cite_note-Snyder1987-1"><span class="cite-bracket">[</span>1<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 {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>s</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3337b739df084a1a6028fbc16f264207f62612ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.453ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi }"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> is constant throughout the map. Here, <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> represents latitude; <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 \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> represents longitude; and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> are the projected (planar) coordinates for a given <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 (\varphi ,\lambda )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>φ</mi> <mo>,</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\varphi ,\lambda )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5156d5f1d8e80e4b3985da59ee883475a84b3ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.719ex; height:2.843ex;" alt="{\displaystyle (\varphi ,\lambda )}"></span> coordinate pair. </p><p>For example, the <a href="/wiki/Sinusoidal_projection" title="Sinusoidal projection">sinusoidal projection</a> is a very simple equal-area projection. Its generating formulae are: </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}x&=R\cdot \lambda \cos \varphi \\y&=R\cdot \varphi \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>x</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>R</mi> <mo>⋅</mo> <mi>λ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mtd> </mtr> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mi>R</mi> <mo>⋅</mo> <mi>φ</mi> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}x&=R\cdot \lambda \cos \varphi \\y&=R\cdot \varphi \end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7d08de05c92a79917b6d8b899d83a7e3107cb43" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.383ex; height:5.843ex;" alt="{\displaystyle {\begin{aligned}x&=R\cdot \lambda \cos \varphi \\y&=R\cdot \varphi \end{aligned}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> is the radius of the globe. Computing the partial derivatives, </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 {\frac {\partial x}{\partial \varphi }}=-R\cdot \lambda \cdot \sin \varphi ,\quad R\cdot {\frac {\partial x}{\partial \lambda }}=R\cdot \cos \varphi ,\quad {\frac {\partial y}{\partial \varphi }}=R,\quad {\frac {\partial y}{\partial \lambda }}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>R</mi> <mo>⋅</mo> <mi>λ</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mo>,</mo> <mspace width="1em" /> <mi>R</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>R</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>R</mi> <mo>,</mo> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial x}{\partial \varphi }}=-R\cdot \lambda \cdot \sin \varphi ,\quad R\cdot {\frac {\partial x}{\partial \lambda }}=R\cdot \cos \varphi ,\quad {\frac {\partial y}{\partial \varphi }}=R,\quad {\frac {\partial y}{\partial \lambda }}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a584fa7efa38ef901eb08750c283939ec550a37" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:64.71ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial x}{\partial \varphi }}=-R\cdot \lambda \cdot \sin \varphi ,\quad R\cdot {\frac {\partial x}{\partial \lambda }}=R\cdot \cos \varphi ,\quad {\frac {\partial y}{\partial \varphi }}=R,\quad {\frac {\partial y}{\partial \lambda }}=0}"></span></dd></dl> <p>and so </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 {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=R\cdot R\cdot \cos \varphi -0\cdot (-R\cdot \lambda \cdot \sin \varphi )=R^{2}\cdot \cos \varphi =s\cdot \cos \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>R</mi> <mo>⋅</mo> <mi>R</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>−</mo> <mn>0</mn> <mo>⋅</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mi>R</mi> <mo>⋅</mo> <mi>λ</mi> <mo>⋅</mo> <mi>sin</mi> <mo>⁡</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>=</mo> <mi>s</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=R\cdot R\cdot \cos \varphi -0\cdot (-R\cdot \lambda \cdot \sin \varphi )=R^{2}\cdot \cos \varphi =s\cdot \cos \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/434f8a766bc5201d702d0e4cc697498532275e34" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:79.609ex; height:6.176ex;" alt="{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=R\cdot R\cdot \cos \varphi -0\cdot (-R\cdot \lambda \cdot \sin \varphi )=R^{2}\cdot \cos \varphi =s\cdot \cos \varphi }"></span></dd></dl> <p>with <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> taking the value of the constant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5ce07e278be3e058a6303de8359f8b4a4288264a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.818ex; height:2.676ex;" alt="{\displaystyle R^{2}}"></span>. </p><p>For an equal-area map of the <a href="/wiki/Ellipsoid" title="Ellipsoid">ellipsoid</a>, the corresponding differential condition that must be met is:<sup id="cite_ref-Snyder1987_1-1" class="reference"><a href="#cite_note-Snyder1987-1"><span class="cite-bracket">[</span>1<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 {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi \cdot {\frac {(1-e^{2})}{(1-e^{2}\sin ^{2}\varphi )^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>φ</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>s</mi> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mi>φ</mi> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>φ</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi \cdot {\frac {(1-e^{2})}{(1-e^{2}\sin ^{2}\varphi )^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c7b3a91a4e65a697a92ee78a25a962f82dde1cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:49.176ex; height:6.843ex;" alt="{\displaystyle {\frac {\partial y}{\partial \varphi }}\cdot {\frac {\partial x}{\partial \lambda }}-{\frac {\partial y}{\partial \lambda }}\cdot {\frac {\partial x}{\partial \varphi }}=s\cdot \cos \varphi \cdot {\frac {(1-e^{2})}{(1-e^{2}\sin ^{2}\varphi )^{2}}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> is the <a href="/wiki/Eccentricity_(mathematics)#Ellipses" title="Eccentricity (mathematics)">eccentricity</a> of the ellipsoid of revolution. </p> <div class="mw-heading mw-heading3"><h3 id="Statistical_grid">Statistical grid</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equal-area_projection&action=edit&section=2" title="Edit section: Statistical grid"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Equal-area_projection&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">April 2020</span>)</i></span></div></td></tr></tbody></table> <p>The term "statistical grid" refers to a <a href="/wiki/Discrete_global_grid" title="Discrete global grid">discrete grid</a> (global or local) of an equal-area surface representation, used for <a href="/wiki/Data_visualization" class="mw-redirect" title="Data visualization">data visualization</a>, <a href="/wiki/Geocode" title="Geocode">geocode</a> and <a href="/wiki/Spatial_analysis" title="Spatial analysis">statistical spatial analysis</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-ibge1_4-0" class="reference"><a href="#cite_note-ibge1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Brodzik_Billingsley_Haran_Raup_2012_pp._32–45_6-0" class="reference"><a href="#cite_note-Brodzik_Billingsley_Haran_Raup_2012_pp._32–45-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="List_of_equal-area_projections">List of equal-area projections</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Equal-area_projection&action=edit&section=3" title="Edit section: List of equal-area projections"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>These are some projections that preserve area: </p> <ul><li>Azimuthal <ul><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/Wiechel_projection" title="Wiechel projection">Wiechel</a> (pseudoazimuthal)</li></ul></li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Albers_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Albers_projection_SW.jpg/300px-Albers_projection_SW.jpg" decoding="async" width="300" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Albers_projection_SW.jpg/450px-Albers_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Albers_projection_SW.jpg/600px-Albers_projection_SW.jpg 2x" data-file-width="2058" data-file-height="1208" /></a><figcaption>Albers projection of the world with standard parallels 20° N and 50° N.</figcaption></figure> <ul><li>Conic <ul><li><a href="/wiki/Albers_projection" title="Albers projection">Albers</a></li> <li><a href="/w/index.php?title=Lambert_equal-area_conic_projection&action=edit&redlink=1" class="new" title="Lambert equal-area conic projection (page does not exist)">Lambert equal-area conic projection</a></li></ul></li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Bottomley_projection_SW.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Bottomley_projection_SW.JPG/300px-Bottomley_projection_SW.JPG" decoding="async" width="300" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Bottomley_projection_SW.JPG/450px-Bottomley_projection_SW.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Bottomley_projection_SW.JPG/600px-Bottomley_projection_SW.JPG 2x" data-file-width="2058" data-file-height="1200" /></a><figcaption>Bottomley projection of the world with standard parallel at 30° N.</figcaption></figure> <ul><li>Pseudoconical <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/Werner_projection" title="Werner projection">Werner</a></li></ul></li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Lambert_cylindrical_equal-area_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Lambert_cylindrical_equal-area_projection_SW.jpg/300px-Lambert_cylindrical_equal-area_projection_SW.jpg" decoding="async" width="300" height="97" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/67/Lambert_cylindrical_equal-area_projection_SW.jpg/450px-Lambert_cylindrical_equal-area_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/67/Lambert_cylindrical_equal-area_projection_SW.jpg/600px-Lambert_cylindrical_equal-area_projection_SW.jpg 2x" data-file-width="2058" data-file-height="664" /></a><figcaption>Lambert cylindrical equal-area projection of the world</figcaption></figure> <ul><li><a href="/wiki/Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Cylindrical</a> (with latitude of no distortion) <ul><li><a href="/wiki/Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert cylindrical equal-area</a> (0°)</li> <li><a href="/wiki/Behrmann_projection" title="Behrmann projection">Behrmann</a> (30°)</li> <li><a href="/wiki/Hobo%E2%80%93Dyer_projection" title="Hobo–Dyer projection">Hobo–Dyer</a> (37°30′)</li> <li><a href="/wiki/Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a> (45°)</li></ul></li></ul> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Equal_Earth_projection_SW.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Equal_Earth_projection_SW.jpg/300px-Equal_Earth_projection_SW.jpg" decoding="async" width="300" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Equal_Earth_projection_SW.jpg/450px-Equal_Earth_projection_SW.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Equal_Earth_projection_SW.jpg/600px-Equal_Earth_projection_SW.jpg 2x" data-file-width="2060" data-file-height="1008" /></a><figcaption>Equal Earth projection, an equal-area pseudocylindrical projection</figcaption></figure> <ul><li>Pseudocylindrical <ul><li><a href="/wiki/Boggs_eumorphic_projection" title="Boggs eumorphic projection">Boggs eumorphic</a></li> <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>, <a href="/wiki/Eckert_IV_projection" title="Eckert IV projection">IV</a> and <a href="/wiki/Eckert_VI_projection" title="Eckert VI projection">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's 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></li> <li>Other <ul><li><a href="/wiki/Eckert-Greifendorff_projection" title="Eckert-Greifendorff projection">Eckert-Greifendorff</a></li> <li>McBryde-Thomas Flat-Polar Quartic Projection<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Hammer_projection" title="Hammer projection">Hammer</a></li> <li><a href="/wiki/Strebe_1995_projection" title="Strebe 1995 projection">Strebe 1995</a></li> <li><a href="/wiki/Snyder_equal-area_projection" title="Snyder equal-area projection">Snyder equal-area projection</a>, used for <a href="/wiki/Geodesic_grid" title="Geodesic grid">geodesic grids</a>.</li></ul></li></ul> <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=Equal-area_projection&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Authalic_latitude" class="mw-redirect" title="Authalic latitude">Authalic latitude</a></li> <li><a href="/wiki/Authalic_radius" class="mw-redirect" title="Authalic radius">Authalic radius</a></li> <li><a href="/wiki/Equiareal_map_(mathematics)" class="mw-redirect" title="Equiareal map (mathematics)">Equiareal map (mathematics)</a></li> <li><a href="/wiki/Measure-preserving_dynamical_system" title="Measure-preserving dynamical system">Measure-preserving dynamical system</a></li> <li><a href="/wiki/Geodesic_polygon_area" class="mw-redirect" title="Geodesic polygon area">Geodesic polygon area</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=Equal-area_projection&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Snyder1987-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Snyder1987_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Snyder1987_1-1"><sup><i><b>b</b></i></sup></a></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="CITEREFSnyder1987" class="citation book cs1">Snyder, John P. (1987). <a rel="nofollow" class="external text" href="https://pubs.er.usgs.gov/publication/pp1395"><i>Map projections — A working manual</i></a>. USGS Professional Paper. Vol. 1395. Washington: United States Government Printing Office. p. 28. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3133%2Fpp1395">10.3133/pp1395</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Map+projections+%E2%80%94+A+working+manual&rft.place=Washington&rft.series=USGS+Professional+Paper&rft.pages=28&rft.pub=United+States+Government+Printing+Office&rft.date=1987&rft_id=info%3Adoi%2F10.3133%2Fpp1395&rft.aulast=Snyder&rft.aufirst=John+P.&rft_id=https%3A%2F%2Fpubs.er.usgs.gov%2Fpublication%2Fpp1395&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEqual-area+projection" class="Z3988"></span></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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210122065047/https://inspire.ec.europa.eu/forum/discussion/view/10928/use-of-the-equal-area-grid-grid-etrs89-laea">"INSPIRE helpdesk | INSPIRE"</a>. Archived from <a rel="nofollow" class="external text" href="https://inspire.ec.europa.eu/forum/discussion/view/10928/use-of-the-equal-area-grid-grid-etrs89-laea">the original</a> on 22 January 2021<span class="reference-accessdate">. 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Arquivo <code>grade_estatistica.pdf</code> em FTP ou HTTP, <a rel="nofollow" class="external text" href="http://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010">Censo 2010</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191202014124/http://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010/">Archived</a> 2 December 2019 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></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 id="CITEREFTsoulos2003" class="citation book cs1">Tsoulos, Lysandros (2003). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/236852866">"An Equal Area Projection for Statistical Mapping in the EU"</a>. In Annoni, Alessandro; Luzet, Claude; Gubler, Erich (eds.). <i>Map projections for Europe</i>. <a href="/wiki/Joint_Research_Centre" title="Joint Research Centre">Joint Research Centre</a>, European Commission. pp. <span class="nowrap">50–</span>55.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=An+Equal+Area+Projection+for+Statistical+Mapping+in+the+EU&rft.btitle=Map+projections+for+Europe&rft.pages=%3Cspan+class%3D%22nowrap%22%3E50-%3C%2Fspan%3E55&rft.pub=Joint+Research+Centre%2C+European+Commission&rft.date=2003&rft.aulast=Tsoulos&rft.aufirst=Lysandros&rft_id=https%3A%2F%2Fwww.researchgate.net%2Fpublication%2F236852866&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEqual-area+projection" class="Z3988"></span></span> </li> <li id="cite_note-Brodzik_Billingsley_Haran_Raup_2012_pp._32–45-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brodzik_Billingsley_Haran_Raup_2012_pp._32–45_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrodzikBillingsleyHaranRaup2012" class="citation journal cs1">Brodzik, Mary J.; Billingsley, Brendan; Haran, Terry; Raup, Bruce; Savoie, Matthew H. (13 March 2012). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fijgi1010032">"EASE-Grid 2.0: Incremental but Significant Improvements for Earth-Gridded Data Sets"</a>. <i>ISPRS International Journal of Geo-Information</i>. <b>1</b> (1). MDPI AG: <span class="nowrap">32–</span>45. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fijgi1010032">10.3390/ijgi1010032</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2220-9964">2220-9964</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=ISPRS+International+Journal+of+Geo-Information&rft.atitle=EASE-Grid+2.0%3A+Incremental+but+Significant+Improvements+for+Earth-Gridded+Data+Sets&rft.volume=1&rft.issue=1&rft.pages=%3Cspan+class%3D%22nowrap%22%3E32-%3C%2Fspan%3E45&rft.date=2012-03-13&rft_id=info%3Adoi%2F10.3390%2Fijgi1010032&rft.issn=2220-9964&rft.aulast=Brodzik&rft.aufirst=Mary+J.&rft.au=Billingsley%2C+Brendan&rft.au=Haran%2C+Terry&rft.au=Raup%2C+Bruce&rft.au=Savoie%2C+Matthew+H.&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Fijgi1010032&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEqual-area+projection" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</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://www.mathworks.com/help/map/flatplrq.html">"McBryde-Thomas Flat-Polar Quartic Projection - MATLAB"</a>. <i>www.mathworks.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">3 January</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.mathworks.com&rft.atitle=McBryde-Thomas+Flat-Polar+Quartic+Projection+-+MATLAB&rft_id=https%3A%2F%2Fwww.mathworks.com%2Fhelp%2Fmap%2Fflatplrq.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AEqual-area+projection" class="Z3988"></span></span> </li> </ol></div> <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 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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-area10" 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_perspective54" 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 href="/wiki/Azimuthal_equidistant_projection" title="Azimuthal equidistant projection">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_metric114" 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 class="mw-selflink selflink">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_construction114" 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="Planar41" 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_also114" 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><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Equal-area_projection&oldid=1268904388">https://en.wikipedia.org/w/index.php?title=Equal-area_projection&oldid=1268904388</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Equal-area_projections" title="Category:Equal-area projections">Equal-area projections</a></li><li><a href="/wiki/Category:Map_projections" title="Category:Map projections">Map projections</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_January_2024" title="Category:Use dmy dates from January 2024">Use dmy dates from January 2024</a></li><li><a href="/wiki/Category:Articles_to_be_expanded_from_April_2020" title="Category:Articles to be expanded from April 2020">Articles to be expanded from April 2020</a></li><li><a href="/wiki/Category:All_articles_to_be_expanded" title="Category:All articles to be expanded">All articles to be expanded</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 12 January 2025, at 03:12<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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