Angle (θ): 0.0°
Point P(x, y): (0, 0)
Revolutions: 0.00
Circle B (Fixed)
Circle A (Rolling)
Cardioid Path
Speed:
1.0x
Visualization Controls
Circle Radius (r)
75 px
Mathematical Context
A Cardioid is an epicycloid produced by a point $P$ on the circumference of a circle of radius $r$ rolling without slipping around a fixed circle of equal radius $r$.
Parametric Equations
x(θ) = r(2 cos θ - cos 2θ)
y(θ) = r(2 sin θ - sin 2θ)
Polar Form
ρ(θ) = 2r (1 - cos θ)
Notice that as Circle A orbits Circle B by angle $\theta$, Circle A rotates by $2\theta$ around its own moving center to satisfy the non-slip condition.