Geometric "proof" by exhaustion

thingiverse

It is challenging to create a volumetric object with orthogonal profiles consisting of a circle, a square, and an equilateral triangle. This project aims to provide a simplified "proof" by exhaustion that such a creation is impossible: each of these shapes has one profile that deviates from perfection. The screenshots display the objects (yellow) in their respective orthogonal views, overlaid with one of the other shapes to illustrate their differences.