Polar Coordinates Grapher
Plot rose curves, cardioids, spirals, lemniscates, and limaçons. Watch the curve trace out as θ sweeps from 0 to 2π.
Polar Curve
Properties
| Curve | -- |
| Equation | -- |
| Shape | -- |
| Symmetry | -- |
| Max r | -- |
The Math Behind It
Polar Coordinates
- A point is described by (r, θ) — distance and angle
- Conversion: x = r·cosθ, y = r·sinθ
- Inverse: r = √(x² + y²), θ = atan2(y, x)
- Curves are defined as r = f(θ)
- As θ sweeps from 0 to 2π, the curve traces out
Common Polar Curves
- Rose: r = a·cos(nθ) — n petals (n odd) or 2n petals (n even)
- Cardioid: r = a(1 + cosθ) — heart-shaped
- Lemniscate: r² = a²·cos(2θ) — figure-eight
- Spiral: r = a·θ (Archimedean) — expands outward
- Limaçon: r = a + b·cosθ — may have inner loop
- Circle: r = a — constant radius
You're crushing it!