“Moser's circle problem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Moser's circle problem

释义

Moser's circle problem

Named after Leo Moser, this result is commonly cited to highlight the need to prove that perceived patterns do indeed continue forever. The maximum number of regions that the chords between n points on a circle divide the interior into is 1, 2, 4, 8, 16 for n = 1, 2, 3, 4, 5. (In the figure n = 4.)

4 points and 8 regions

It would seem reasonable to suppose the pattern continues as 2n–1, but in fact the next term is 31, and the nth term of the sequence is

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