_notpalindrome_'s blog

By _notpalindrome_, history, 15 months ago, In English,

Can anyone please explain me easier way the question (question link given below). I didnt understand the question since my geometry knowledge is very low. Also It would be great if you explain also the solution for the problem actually I didnt solve any problem from geometry.

Sorry for my poor English. Thanks In Advance https://codeforces.com/contest/1096/problem/C

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15 months ago, # |
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What exactly you can't understand exactly? Which sentence in the problem description?

We can't explain everything, and most of the definitions are available on Wikipedia anyway, see https://en.wikipedia.org/wiki/Regular_polygon for example.

15 months ago, # |
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Without losing generality, it can be assumed that a regular polygon G with n ≥ 3 vertices is centered at the origin, and that it is circumscribed by a unit circle with radius R = 1 that passes through all these vertices. Note that G consists of n identical isosceles triangles with angles {90 - 180 / n, 90 - 180 / n, 360 / n} degrees and sides {1, 1, 2 sin(π / n)}. Vertices of G can be enumerated as V = {0, 1, ..., n - 1}, such that vertex is located at polar angle θi = 360 × i / n. Let us assume that the triple T = {a, b, c} is a subset of V such that 0 ≤ a < b < c ≤ n - 1. It can be shown that , where k = c - a and 2 ≤ k ≤ n - 1. In fact, is an incsrcibed angle whose value depends on the polar angle difference between c and a, and is independent of the location of b. The problem is then reduced to the simpler problem of finding the smallest n ≥ 3 for the given integer degrees that satisfies the previous equation.

The following is a C++14 program that generates all the 22 minimum-size regular polygons that include all inscribed angles . The list next to each polygon is the values of the inscribed angle(s) that such polygon includes.