Animated tracing, area shading & coordinate conversion
Polar coordinates use (r, θ) where r is the distance from the origin and θ is the angle from the positive x-axis. Classic polar curves include the cardioid r = a(1+cosθ), rose curves r = a·cos(nθ), the Archimedean spiral r = aθ, the lemniscate r² = a²·cos(2θ), and the limaçon r = 1+a·cosθ. Press Animate to watch the tracing dot draw the curve!