Description from <a href="//commons.wikimedia.org/w/index.php?title=Template:Archimedes_spiral_with_sector.PNG&amp;action=edit&amp;redlink=1" class="new" title="Template:Archimedes spiral with sector.PNG (page does not exist)">Template:Archimedes spiral with sector.PNG</a>:
Archimedes' spiral with a sector <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 M_{1}OM_{2}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>M</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mi>O</mi><msub><mi>M</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle M_{1}OM_{2}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23469672eaa1e008dafdbdb7a3093f056a235cbe" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:8.39ex; height:2.509ex;" alt="{\displaystyle M_{1}OM_{2}}"></span> which surface is calculated due to the formula <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={\frac {a^{2}}{6}}({\varphi _{2}}^{3}-{\varphi _{1}}^{3})}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>S</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><msup><mi>a</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mn>6</mn></mfrac></mrow><mo stretchy="false">(</mo><msup><mrow class="MJX-TeXAtom-ORD"><msub><mi>φ<!-- φ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msub></mrow><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo>−<!-- − --></mo><msup><mrow class="MJX-TeXAtom-ORD"><msub><mi>φ<!-- φ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mrow><mrow class="MJX-TeXAtom-ORD"><mn>3</mn></mrow></msup><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle S={\frac {a^{2}}{6}}({\varphi _{2}}^{3}-{\varphi _{1}}^{3})}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b860cc481b27612b47b025a251d5289bda89e706" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.838ex; width:19.625ex; height:5.676ex;" alt="{\displaystyle S={\frac {a^{2}}{6}}({\varphi _{2}}^{3}-{\varphi _{1}}^{3})}"></span>
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2014-04-10
<span class="int-own-work" lang="en">Own work</span>