Valentine's Day — The Heart Curve

The equation (x² + y² − 1)³ = x²y³ draws a perfect heart shape when plotted. In polar coordinates, r = 1 − sin(θ) creates a cardioid — literally 'heart-shaped' in Greek. The cardioid appears naturally in the boundary of the Mandelbrot set, in the reflection patterns inside a coffee cup in sunlight, and in the caustic curves of optics. When two circles of equal radius roll around each other, one point on the rolling circle traces a cardioid. Mathematics has its own Valentine.