Archimedean circle

In geometry, an Archimedean circle is defined in an arbelos as any circle with a radius "ρ" where:$ho=frac\{1\}\{2\}rleft(1-r\; ight).$There are over fifty different known ways to construct Archimedean circles. [citeweb| url=http://home.wxs.nl/~lamoen/wiskunde/Arbelos/Catalogue.htm| title=Online catalogue of Archimedean circles| accessdate=2008-08-26]

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. [Cite web|url=http://www.retas.de/thomas/arbelos/biola/index.html|title=A Dozen More Arbelos Twins|accessdate=2008-08-30|author=Thomas Schoch|date=1998] [Cite web|url=http://www.retas.de/thomas/arbelos/Ubiquitous.pdf|title=Those Ubiquitous Archimedean Circles|accessdate=2008-08-30|author=Clayton W. Dodge, Thomas Schoch, Peter Y. Woo, Paul Yiu|date=1999] He also constructed what is known as the Schoch line. [citeweb|author=van Lamoen, Floor|title=Schoch Line." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein|url=http://mathworld.wolfram.com/SchochLine.html|accessdate=2008-08-26]

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. [Cite web|url=http://www.retas.de/thomas/arbelos/woo.html|title=Arbelos - The Woo Circles|accessdate=2008-08-26|author=Thomas Schoch|date=2007]

Frank Power

In the summer of 1998, Frank Power introduced four more Archimedes circles known as Archimedes' quadruplets. [citation| last=Power| first=Frank| title=Forum Geometricorum| volume=5| chapter=Some More Archimedean Circles in the Arbelos| date=2005| publication-date=2005-11-02| editor-last=Yiu| editor-first=Paul| pages=133-134| isbn=1534-1178| url=http://forumgeom.fau.edu/FG2005volume5/FG200517.ps| accessdate=2008-06-26]

References