更新1:
六呎將軍,看不到你的一些圖片。
數學高難度題目(一)
2009-02-15 7:32 pm
Given a string of length l , state and explain which shape formed that can have a maximum area ,also find this maximum area in terms of l .
回答 (3)
2009-02-15 9:23 pm
✔ 最佳答案
The shape should be in regular polygon. Starting from a square and a regular pentagon, we have:http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom2.jpg
http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom3.jpg
http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom4.jpg
http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom5.jpg
So f(x) is strictly increasing and so, when n is larger, An will also be larger.
Finally, taking limit of n → ∞, we can find out that the largest possible area will be:
http://i388.photobucket.com/albums/oo325/loyitak1990/Feb09/Crazygeom6.jpg
which is in fact, a circle in shape.
2009-02-15 14:21:08 補充：
搞掂, 請 reload.
參考: Myself
2009-02-15 9:14 pm
he is correct
2009-02-15 8:44 pm
Max. area formed is a circle.
radius = l/2*pi
area = l^2/(4*pi)
radius = l/2*pi
area = l^2/(4*pi)
收錄日期: 2021-04-22 00:34:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090215000051KK00622