what is the greatest number of parts a circle can be cut into using 6 strainght cut?
Please show the working out, draw a diagram
Can someone help me
2008-03-06 11:04 pm
回答 (1)
2008-03-07 1:03 am
✔ 最佳答案
let n be the number of lineslet A be the number of regions
when n=1, A=2
when n=2, A=4=2+2
when n=3, A=7=4+3
when n=4, A=11=7+4
when n=5, A=16=11+5
when n=6, A=22=16+6
so when n=k, A=2+2+3+4+...+(k-2)(k-1)+k
you may see that (A-1) is a trangular number
i.e. A=n(n+1)/2 +1
image:
http://i256.photobucket.com/albums/hh182/zilu_photo/d14fe604.jpg
圖片參考：http://i256.photobucket.com/albums/hh182/zilu_photo/d14fe604.jpg
參考: my maths knowledge
收錄日期: 2021-04-13 18:45:00
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080306000051KK01044