It’s well known that you can’t use a ruler and compass to construct a square with the same area as a given circle. But did you know that you can use a ruler and compass to construct a square with the same area as a given rectangle? Or triangle? Or other polygon?
I wrote some python code to animate some of these constructions. There are a couple of examples at the end of the post. You might find this interesting or useful – if so, I invite you to download it and play around. The code is offered as-is; I wrote it for my personal use, so it is messy and undocumented, has no error handling and is probably full of bugs. But if you can put up with all that then feel free to use it.
Download the code from github.com/SamHartburn/RulerCompassAnimations.