I’ve always enjoyed playing around with pinscreens, but only recently did I realize what cool mathematical concepts they display!
For example, the image above shows an approximation of the volume of a hemisphere using right cylinders. A pinscreen Riemann sum!
And the images below suggest how we might approximate the areas of a circle and a square using pinscreens.
Compute the ratio of raised pins to total pins, and multiply by the total area of the pinscreen. A pinscreen Monte Carlo method!
Any other cool math hiding in there?