A <a href="https://en.wikipedia.org/wiki/Curve_of_constant_width" class="extiw" title="en:Curve of constant width">curve of constant width</a> (yellow shaded region) generated by intersecting circular disks (blue) centered on the points of a <a href="https://en.wikipedia.org/wiki/Semi-ellipse" class="extiw" title="en:Semi-ellipse">semi-ellipse</a> (black). The width of the curve equals the chord of the starting arc. This construction works for any arc whose curvature is high enough for it to be contained in every circle tangent to one of its supporting lines, with radius equal to the chord length; one of these tangent circles, at a point of minimum curvature of the semi-ellipse, is shown in red. The eccentricity of the ellipse, <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 {\tfrac {1}{2}}{\sqrt {3}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="false" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle></mrow><mrow class="MJX-TeXAtom-ORD"><msqrt><mn>3</mn></msqrt></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{2}}{\sqrt {3}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69ed0b8e310a3c4fd60d8eba24dc63f326b5cf19" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:4.756ex; height:3.509ex;" alt="{\displaystyle {\tfrac {1}{2}}{\sqrt {3}}}"></span>, is the maximum value that meets this curvature condition.
<a href="//commons.wikimedia.org/wiki/User:David_Eppstein" class="mw-redirect" title="User:David Eppstein">David Eppstein</a>
<span class="int-own-work" lang="en">Own work</span>