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.

Open Visualizer