Discussion @ 1020. Rope @ Timus Online Judge

mathematical proof

Posted by emilchess 6 Nov 2012 02:31

Draw a polygon. the sum of its angles is pi*(n-2). The sum of pieces of circles is R*(n*pi-(n-2)*pi)=2*R*pi (you can see it easily if u draw)

Re: mathematical proof

Posted by Ouch 7 Nov 2013 14:20

Thanks, so nice.

Re: mathematical proof

Posted by prostack 2 Feb 2014 08:46

yep, its simple

Re: mathematical proof

Posted by lakerka 22 Mar 2015 17:54

Beautiful. Solved it by calculating angles between vectors of consecutive nails.

Re: mathematical proof

Posted by Abdul Matin 6 Oct 2018 22:57

How is the sum of its angles pi*(n-2)?

Re: mathematical proof

Posted by crvdgc 10 Mar 2019 18:29

OP means the sum of angles in a n-polygon is pi*(n-2). This can be attained inductively:
1. The sum of angles in a triangle is pi.
2. for any n-polygon, it can be divided into a (n-1)-polygon and a triangle.

Re: mathematical proof

Posted by _confused 3 Dec 2020 21:53

thanks !

Discussion of Problem 1020. Rope