In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
, the Schoch circles are twelve
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. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and '' ...
s constructed by Thomas Schoch.
History
In 1979, Thomas Schoch discovered a dozen new Archimedean circles; he sent his discoveries to ''
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
s "Mathematical Games" editor
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...
. The manuscript was forwarded to
Leon Bankoff
Leon Bankoff (December 13, 1908 – February 16, 1997), born in New York City, New York, was an American dentist. As an amateur mathematician he constructed the Bankoff circle. He was also an Esperantist.
Life
After a visit to the City ...
. Bankoff gave a copy of the manuscript to Professor Clayton Dodge of the
University of Maine
The University of Maine (UMaine or UMO) is a public land-grant research university in Orono, Maine. It was established in 1865 as the land-grant college of Maine and is the flagship university of the University of Maine System. It is classifie ...
in 1996. The two were planning to write an article about the Arbelos, in which the Schoch circles would be included; however, Bankoff died the year after.
In 1998, Peter Y. Woo of
Biola University
Biola University () is a private, nondenominational, evangelical Christian university in La Mirada, California. It was founded in 1908 as the Bible Institute of Los Angeles. It has over 150 programs of study in nine schools offering bachelor's ...
published Schoch's findings on his website. By generalizing two of Schoch's circles, Woo discovered an infinite family of Archimedean circles named the
Woo circles in 1999.
Circles
Image:Schoch circles 1 and 2.svg, Circles a and b
Image:Schoch circles 3 and 4.svg, Circles c and d
Image:Schoch circles 5.svg, Circle e
Image:Schoch circles 6 and 7.svg, Circles f and g
Image:Schoch circles 8.svg, Circles h
Image:Schoch circles 9 and 10.svg, Circles i and j
Image:Schoch circles 11 and 12.svg, Circles k and l
See also
*
Schoch line
References
External links
{{commons category
Online catalogue of Archimedean circles*Hiroshi Okumura and Masayuki Watanabe (2004).
The Archimedean Circles of Schoch and Woo. Forum Geometricorum Volume 4.
Arbelos
de:Archimedischer Kreis#Schoch-Kreise und Schoch-Gerade