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In mathematics, more specifically, in convex geometry, the mixed volume is a way to associate a non-negative number to an ''n''-tuple of convex bodies in the ''n''-dimensional space. This number depends on the size of the bodies and their relative positions. ==Definition== Let ''K''1, ''K''2, ..., ''K''''r'' be convex bodies in R''n'', and consider the function : where Vol''n'' stands for the ''n''-dimensional volume and its argument is the Minkowski sum of the scaled convex bodies ''Ki''. One can show that ''f'' is a homogeneous polynomial of degree ''n'', therefore it can be written as : where the functions ''V'' are symmetric. Then ''V''(''T''1, ..., ''T''''n'') is called the mixed volume of ''T''1, ''T''2, ..., ''T''''n''. Equivalently, : 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「mixed volume」の詳細全文を読む スポンサード リンク
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