Обсуждение @ 1020. Ниточка @ Timus Online Judge

emilchess mathematical proof [6] // Задача 1020. Ниточка 6 ноя 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)

Ouch Re: mathematical proof [1] // Задача 1020. Ниточка 7 ноя 2013 14:20

Thanks, so nice.

prostack Re: mathematical proof // Задача 1020. Ниточка 2 фев 2014 08:46

yep, its simple

lakerka Re: mathematical proof // Задача 1020. Ниточка 22 мар 2015 17:54

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

Abdul Matin Re: mathematical proof [2] // Задача 1020. Ниточка 6 окт 2018 22:57

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

crvdgc Re: mathematical proof [1] // Задача 1020. Ниточка 10 мар 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.

_confused Re: mathematical proof // Задача 1020. Ниточка 3 дек 2020 21:53

thanks !

Обсуждение задачи 1020. Ниточка