EPICYCLOID & HYPOCYCLOID

A circle rolls on the outside (epi) or inside (hypo) of a fixed circle, tracing beautiful curves.
Special cases: cardioid, nephroid, deltoid, astroid.

TYPE

k = R/r: 3

ANIMATE

TANGENTS

Epicycloid: x = (R+r)cos(t) − r·cos((R+r)t/r) | Arc length = 8nR | Area = πR²(k²+4k+3) / wait, A = πr²(k+1)²·... exploring!