I was watching a video; the amount of collisions made between two colliding blocks on a frictionless surface with walls on either side that have infinite mass always equals the digits of pi. So say one block is 100kg (block A) and the other is 1kg (block B) and we are assuming perfectly elastic collisions, the total amount of collisions before block Ahits the opposite wall would be 31. We keep increasing block A’s mass and the numbers go up: ex. 314 at 10 000kg, 3141 at 1 000 000kg.
After that video I tried to understand *why* this happens but I am no mathematics expert. If we’re being honest here “elastic collisions” was a stretch for me haha I had to reach back to my high school physics memories.
In: 323
The connection comes from the following.
As we all now, pi comes from circles. A circle of radius 1 is defined as the set of all points with a distance of 1 to the origin ( (0,0) coordinates). Notice that if you draw a line from the origin to a point, you can effectively imagine a right triangle. The side you just drew is the hypotenuse and the two legs are given by the x and y coordinates of the point. So the distance of a point to the origin is the hypotenuse of this triangle. By the Pythagorean theorem, we can work it out now!
x² + y² = c². A circle is the set of all points such that the distance to the origin (in other words, c) is 1 so its the set of all points which satisfy x² + y² = 1². Or we can just write x² + y² = 1.
The connection between circles and this problem comes from the fact that kinetic energy is conserved in this system. The physics equation describing that coincidentally also looks something like the circle equation: (energyOfFirstBlock)² + (energyOfSecondBlock)² = 1. The equation effectively says that the total amount of energy stays constant at 1, but the energy can be freely distributed among the 2 blocks. It just so happens that this is also the equation for a circle of radius 1.
This should give you an idea where pi would even come from. Explaining why pi shows up _like that_ is more complicated so I wont go into it here. Also, my math should check out but please correct my physics if I said something incorrect.
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