Parametric powers / 03
Astroid & Power Curves
Geometry
Raise sine and cosine to the same integer power n. Power 1 gives a circle, power 2 a segment, and power 3 an astroid. Odd powers preserve signs; even powers stay in the first quadrant.
x(t) = R·cos(t)^n
y(t) = R·sin(t)^n
Adjust power to explore · Animate traces the curve · GIF sweeps integer powers 1–12