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In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle. ==Properties== If the smaller circle has radius ''r'', and the larger circle has radius ''R'' = ''kr'', then the parametric equations for the curve can be given by either: : : or: : : If ''k'' is an integer, then the curve is closed, and has ''k'' cusps (i.e., sharp corners, where the curve is not differentiable). Specially for k=2 the curve is a straight line and the circles are called Cardano circles. Girolamo Cardano was the first to describe these hypocycloids and their applications to high-speed printing. If ''k'' is a rational number, say ''k'' = ''p''/''q'' expressed in simplest terms, then the curve has ''p'' cusps. If ''k'' is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius ''R'' − 2''r''. Each hypocycloid (for any value of ''r'') is a brachistochrone for the gravitational potential inside a homogeneous sphere of radius ''R''. 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「hypocycloid」の詳細全文を読む スポンサード リンク
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