Why colliding blocks compute pi

Summary by Krater

This video explains the surprising mathematical connection between the number of block collisions on a frictionless plane and the digits of pi, using conservation of energy and momentum, state space analysis, and the inscribed angle theorem.

From the video

Answers: Why do block collisions compute the digits of pi?

• block collision physics puzzle
• conservation of energy and momentum
• state space analysis of velocities
• connection between block collisions and pi
• inscribed angle theorem applied to collision angles

What it concludes

• As the mass of the larger block increases by powers of 100, the total number of collisions between the two blocks and the wall matches the digits of pi.
• Using conservation of energy and momentum, the collision physics can be mapped to an ellipse in a velocity coordinate system, which can be rescaled into a circle.
• The problem of counting collisions in physics transforms into a pure geometry problem of counting how many times a line bounces inside a circle.
• Using the inscribed angle theorem, the angle subtended by each bounce on the circle is equal to two times the angle theta, which is determined by the mass ratio.
• The maximal number of times the line can bounce before entering the end zone equals the digits of pi when the mass ratio is a power of 100.