Обсуждение @ 1020. Ниточка @ Timus Online Judge

Metalmax Why 2*Pi*R ? [4] // Задача 1020. Ниточка 31 окт 2004 17:24

I solve that problem but I don't understand why I should take 2*Pi*R ?
I know that the center length of the center of the nails is:
sqrt((x2-x1)^2 + (y2-y1)^2)
but why 2*PI*R ??????

Edited by author 31.10.2004 17:26

Nguyen Duc Dung Re: Why 2*Pi*R ? [3] // Задача 1020. Ниточка 2 ноя 2004 14:56

help me. i can't solve this problem.

Aleksandr Re: Why 2*Pi*R ? [2] // Задача 1020. Ниточка 6 май 2006 20:20

2PiR is length of arc's

Machvi Re: Why 2*Pi*R ? [1] // Задача 1020. Ниточка 8 фев 2007 02:55

it has a very nice solution

svr Re: Why 2*Pi*R ? // Задача 1020. Ниточка 8 фев 2007 10:08

You should find explanations to the formula to not
it be trick.
For example. Let us consider inner normal vector to the boundary - n , moving along boundary. It gets rotation 2*Pi after one circle. But really n rotates only on angles or on
archs and total rotation is L/R where L- total length of archs . Thus we have 2*Pi=L/R therefore L=2*Pi*R

Обсуждение задачи 1020. Ниточка