When Math Gets Loopy: The Spirograph Equation
·47 words·1 min
Spirograph equation:
x(t) = (R+r)*cos(t) - (r+a)*cos(((R+r)*t)/r) y(t) = (R+r)*sin(t) - (r+a)*sin(((R+r)*t)/r)
R: fixed circle radius r: moving circle radius (-ve if its outside of fixed circle) a: pen distance from origin in moving circle t: angle = 0 to 2 * pi * LCM(r, R)/r