# Definition:Archimedean Spiral

## Definition

The **Archimedean spiral** is the locus of the equation expressed in Polar coordinates as:

- $r = a \theta$

### Archimedes' Definition

*If a straight line of which one extremity remains fixed be made to revolve at a uniform rate in a plane until it returns to the position from which it started, and if, at the same time as the straight line revolves, a point moves at a uniform rate along the straight line, starting from the fixed extremity, the point will describe a spiral in the plane.*

## Also known as

Some sources render this as a **spiral of Archimedes**.

## Source of Name

This entry was named for Archimedes of Syracuse.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*: $11.35$: Special Plane Curves - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $287$ – $212$ B.C.) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $6$: Curves and Coordinates - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Archimedean spiral**