# 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

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.[1]

## 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.

### Thomas Schoch

In 1978 Thomas Schoch found a dozen more Archimedean circles (the Schoch circles) that have been published in 1998.[2][3] He also constructed what is known as the Schoch line.[4]

### 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.[5]

### Frank Power

In the summer of 1998, Frank Power introduced four more Archimedes circles known as Archimedes' quadruplets.[6]

## References

- "Online catalogue of Archimedean circles". Retrieved 2008-08-26.
- Thomas Schoch (1998). "A Dozen More Arbelos Twins". Retrieved 2008-08-30.
- Clayton W. Dodge; Thomas Schoch; Peter Y. Woo; Paul Yiu (1999). "Those Ubiquitous Archimedean Circles" (PDF). Retrieved 2008-08-30.
- van Lamoen, Floor. "Schoch Line." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein". Retrieved 2008-08-26.
- Thomas Schoch (2007). "Arbelos - The Woo Circles". Archived from the original on 2014-08-14. Retrieved 2008-08-26.
- Power, Frank (2005). "Some More Archimedean Circles in the Arbelos". In Yiu, Paul (ed.).
*Forum Geometricorum*.**5**(published 2005-11-02). pp. 133–134. ISSN 1534-1178. Retrieved 2008-06-26. - Okumura, Hiroshi (2019). "Remarks on Archimedean circles of Nagata and Ootoba". In Okumura, Hiroshi (ed.).
*Sangaku Journal of Mathematics*(PDF).**3**(published 2019-11-04). pp. 119–122. ISSN 2534-9562. Retrieved 2019-11-04.