CorePolar
Cardioid
r = a(1 + cos θ)
Overview
A cardioid is a heart-shaped curve formed by a point on a rolling circle.
Domain
θ ∈ [0, 2π]
Range
r ∈ [0, 2a]
Key Properties
1
Heart-shaped with cusp at origin
2
Maximum r = 2a at θ = 0
3
Used in microphone pickup patterns
4
Also appears in caustics and Mandelbrot set
Key Insight
The cardioid appears in the Mandelbrot set boundary — mathematics connects in beautiful ways!
Visualize Cardioid
Interact with the graph and explore this curve in the analytic geometry visualizer.