# Archimedean circle

In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. The radius ρ of such a circle is given by

$\rho ={\frac {1}{2}}r\left(1-r\right),$ where r is the ratio AB/AC shown in the figure to the right. There are over fifty different known ways to construct Archimedean circles.

## Origin

An Archimedean circle was first constructed by Archimedes in his Book of Lemmas. In his book, he constructed what is now known as Archimedes' twin circles.

## Other Archimedean circles finders

### Leon Bankoff

Leon Bankoff has constructed other Archimedean circles called Bankoff's triplet circle and Bankoff's quadruplet circle.

The Schoch line (cyan line) and examples of Woo circles (green).

### Thomas Schoch

In 1978 Thomas Schoch found a dozen more Archimedean circles (the Schoch circles) that have been published in 1998. He also constructed what is known as the Schoch line.

### Peter Y. Woo

Peter Y. Woo considered the Schoch line, and with it, he was able to create a family of infinitely many Archimedean circles known as the Woo circles.

### Frank Power

In the summer of 1998, Frank Power introduced four more Archimedes circles known as Archimedes' quadruplets.

### Archimedean circles in Wasan geometry (Japanese geometry)

In 1831, Nagata (永田岩三郎遵道) proposed a sangaku problem involving two Archimedean circles, which are denoted by W6 and W7 in . In 1853, Ootoba (大鳥羽源吉守敬) proposed a sangaku problem involving an Archimedean circle.