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.

Also see

• Results about Archimedean spirals can be found here.

Source of Name

This entry was named for Archimedes of Syracuse.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Cissoid of Diocles: $11.35$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Archimedean spiral
• 1991: David Wells: Curious and Interesting Geometry: Archimedean spiral
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Archimedean spiral
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): spiral
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Archimedean spiral
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spiral
• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $6$: Curves and Coordinates: Cartesian coordinates
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Archimedean spiral