回複：更有意思的題，最多幾個銳角？

來源: 好吃客 於 2010-07-21 06:42:43 [] [舊帖] [給我悄悄話] 閱讀數 : (688 bytes)

For convex polygons, There are at most 3 acute angles.

1. Assume that all angles in a n-sided convex are acute. Total interior angles will be less than 90*n. Since the total interior angle of a polygon equals 180*(n-2), we have 2*(n-2)
2. For n>=4, there is at least 1 obtuse angle. Assume the number of obtuse angle as m. Total interior angles will be (m obtuse angles + (n-m) acute angles ) which is less than m*180+(n-m)*90. Since the total interior angle equals 180*(n-2), we have 180*(n-2)

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