7
votes
3answers
688 views

Project Euler Question 222

Would I be wrong to assume that the solution to this problem: What is the length of the shortest pipe, of internal radius 50mm, that can fully contain 21 balls of radii 30mm, 31mm, ..., 50mm? ...
1
vote
0answers
284 views

Number of closed paths formed by arcs of one fifth of a circle

**I was trying to solve the following issue: Find the number of possible closed paths using one fifth of an arc (72 degrees), where at each time step we can move either clockwise or anti-clockwise. ...
2
votes
3answers
559 views

Primitive integer triangles

Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1. How many primitive integer sided triangles exist with a ...
3
votes
4answers
8k views

How to calculate reflected light angle?

On a 2D plane, line X is at x radians angle, an incoming light travels at y radians angle, how to calculate the angle of the outgoing light reflected off line X? How to do this in a way to cover all ...