1 Can you find a formula to compute the max number of angles that are bigger than 180 degree in concave n-gon? For example, when n=4, the answer is 1; when n=5 or 6, the answer is 2.
2 In a concave n-gon, no 3 points are colinear. Is it sometimes possible to use the vertices of this n-gon to form a new n-gon such that the number of angles that are bigger than 180 degree is different from the old n-gon?
Note: the angles are inner angles which is the default meaning.
yma16, there is something I can't understand .....（图）
In your question #1, you said, "when n=5 or 6, the answer is 2". Why when n=6, the max number of angles that are bigger than 180 degree is not 3? Seems we can draw a concave 6-gon with the max number of angles that are bigger than 180 degree being 3 easily, see below (I don't know if my plot can be shown or not):
回复：yma16, there is something I can't understand ..
Sorry, that is my mistake. The formula is n-3.
For part 2, you can try points (2,1), (-2,1), (1,0), (-1,0), (2,-1), and (-2, -1). These points can give you 2 angles > 180 degree or 1 angles > 180 degree.
哈哈哈哈 O(∩_∩)O哈哈~ 好久不来了，不小心看了一眼自己主页，发现自动关联了自己以往发过的帖，点进这个看了一眼，笑个半死。。。敢情我当初还发过这么搞笑的东西啊，我自己完全不记得了 
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发表于 2005-8-17 19:33:51
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千斤顶
发表于 2005-8-18 05:32:49
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