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In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center.〔(【引用サイトリンク】url=http://mathworld.wolfram.com/CircleEvolute.html )〕 Equivalently, an evolute is the envelope of the normals to a curve. The evolute of a curve, a surface, or more generally a submanifold, is the caustic of the normal map. Let ''M'' be a smooth, regular submanifold in R''n''. For each point ''p'' in ''M'' and each vector v, based at ''p'' and normal to ''M'', we associate the point . This defines a Lagrangian map, called the normal map. The caustic of the normal map is the evolute of ''M''. ==History== Apollonius (c. 200 BC) discussed evolutes in Book V of his ''Conics''. However, Huygens is sometimes credited with being the first to study them (1673). Huygens formulated his theory of evolutes sometime around 1659 to help solve the problem of finding the tautochrone curve, which in turn helped him construct an isochronous pendulum. This was because the tautochrone curve is a cycloid, and the cycloid has the unique property that its evolute is also a cycloid. The theory of evolutes, in fact, allowed Huygens to achieve many results that would later be found using calculus. 〔Yoder, Joella G. Unrolling Time: Christiaan Huygens and the Mathematization of Nature. Cambridge University Press, 2004. 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「evolute」の詳細全文を読む スポンサード リンク
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