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In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere (i.e., the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere). It is a counterintuitive fact that this volume does not depend on the original sphere's radius but only on the resulting band's height. The problem is so called because after removing a cylinder from the sphere, the remaining band resembles the shape of a napkin ring. == Statement == Suppose the axis of a right circular cylinder passes through the center of a sphere of radius ''R'' and that ''h'' represents the height (defined as the distance in a direction parallel to the axis) of the part of the boundary of the cylinder that is inside the sphere. The "band" is the part of the sphere that is outside the cylinder. The volume of the band depends on ''h'' but not on ''R'': : As the radius ''R'' of the sphere shrinks, the diameter of the cylinder must also shrink in order that ''h'' can remain the same. The band gets thicker, and that would increase its volume. But it also gets shorter in circumference, and that would decrease its volume. The two effects exactly cancel each other out. In the most extreme case, involving the smallest possible sphere, the cylinder vanishes and the height ''h'' would equal the diameter of the sphere. In that case the volume of the band is the volume of the whole sphere, which matches the formula given above. An early study of this problem was written by 17th-century Japanese mathematician Seki Kōwa. According to , Seki called this solid an arc-ring, or in Japanese ''kokan'' or ''kokwan''. 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「Napkin ring problem」の詳細全文を読む スポンサード リンク
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