IntroPolar
Spiral
r = aθ
Overview
The Archimedean spiral winds outward as the angle increases.
Domain
θ ∈ [0, ∞)
Range
r ∈ [0, ∞)
Key Properties
1
r increases linearly with θ
2
Spacing between turns is constant (2πa)
3
Starts at origin when θ = 0
4
Used in springs, coils, and galaxy arms
Key Insight
The spiral of a vinyl record groove is approximately Archimedean — constant spacing between tracks.
Visualize Spiral
Interact with the graph and explore this curve in the analytic geometry visualizer.