mathematical proof

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

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

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.