Tumble

a shape rolls the way its corners let it.

three chalk shapes on a slate: drag one and it lurches corner to corner; tap it to add sides until it rolls like a wheel

In Everything, nothing walks: a deer, a boulder and a galaxy all get about by tumbling end over end, and the deer clunks where the pebble rolls. That is geometry, not animation. A rigid shape rolling on flat ground pivots on whichever corner is touching, and its centre stays exactly one radius from that corner, so it climbs up over the corner and drops onto the next edge. The size of that drop is R(1 − cos π/n): half a radius for a triangle, a twentieth for a twelve-sided shape, nothing at all for a circle. Here three chalk shapes roll under your finger and leave a trace of where their centre went, and every side you add flattens that trace a little more.

its centre stays one radius from the corner it stands on. more corners, less to climb.

Concepts: geometry, motion.

An interactive you play with one thumb, on Wundr.