This is not a computer story but it fits here anyway.

I had to take a ‘wood shop’ course in high school. One day the teacher said he would bring in a tool to drill a square hole. I though he was pulling our legs as in ‘sand-paper sharpener’. The next day he indeed brought a tool that fit on our standard drill press and with it quickly drilled a square hole in an ordinary piece of wood. The size of the hole was about 3/8 inch. The operation was no noisier than drilling an ordinary hole. The press did not vibrate.

The teacher did not let us examine the tool but promised that we could the next day. I did not like wood shop but I looked forward to the next day. It was not very clear how the tool worked but years later I learned the math that explains everything:

A constant width curve is part of the solution. The indicated article shows how a somewhat triangular shape can rotate smoothly in a square. This shape does not get into the corners however.

See too this. See this marvelous animation from Russia.