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Laser Beams and Elliptical Billiards: Euler Problem 144

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Euler problem 144 has been one of the most fun to solve. The underlying problem is the pathway of the reflection of a laser inside an ellipse-shaped mirror. Before I delve into this problem, I like to share this delightful video from Numberphile in which Alex Bellos demonstrates an elliptical billiards table. The billiards problem is mathematically equivalent to the laser problem. The reflection rule optics is the same as the bouncing rule in mechanics, but instead of using light, we use a billiard ball. This article outlines my solution to Euler problem 104 and simulates the elliptical pool table in the R language. You can find the code on the GitHub repository for this website. Euler Problem 144 Definition In laser physics, a “white cell” is a mirror system that acts as a delay line for the…
Original Post: Laser Beams and Elliptical Billiards: Euler Problem 144