In
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
, the Schoch circles are twelve
Archimedean circles 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 scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it, with more than 150 Nobel Pri ...
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 magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...
. The manuscript was forwarded to
Leon Bankoff. Bankoff gave a copy of the manuscript to Professor Clayton Dodge of the
University of Maine
The University of Maine (UMaine) is a Public university, public Land-grant university, land-grant research university in Orono, Maine, United States. It was established in 1865 as the land-grant college of Maine and is the Flagship universitie ...
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' ...
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