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In elementary geometry, the pizza theorem states the equality of two areas that arise when one partitions a disk in a certain way. Let ''p'' be an interior point of the disk, and let ''n'' be a number that is divisible by four and greater than or equal to eight. Form ''n'' sectors of the disk with equal angles by choosing an arbitrary line through ''p'', rotating the line ''n''/2 − 1 times by an angle of 2π/''n'' radians, and slicing the disk on each of the resulting ''n''/2 lines. Number the sectors consecutively in a clockwise or anti-clockwise fashion. Then the pizza theorem states that: :'' The sum of the areas of the odd numbered sectors equals the sum of the areas of the even numbered sectors'' . The pizza theorem is so called because it mimics a traditional pizza slicing technique. It shows that, if two people share a pizza sliced in this way by taking alternating slices, then they each get an equal amount of pizza. ==History== The pizza theorem was originally proposed as a challenge problem by ; the published solution to this problem, by Michael Goldberg, involved direct manipulation of the algebraic expressions for the areas of the sectors. provide an alternative proof by dissection: they show how to partition the sectors into smaller pieces so that each piece in an odd-numbered sector has a congruent piece in an even-numbered sector, and vice versa. has given a family of dissection proofs for all cases (in which the number of sectors is 8, 12, 16, ...). 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「Pizza theorem」の詳細全文を読む スポンサード リンク
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