Schoch circles
Encyclopedia
In geometry
, the Schoch circles are twelve Archimedean circles constructed by Thomas Schoch.
's "Mathematical Games" editor Martin Gardner
. The manuscript was forwarded to Leon Bankoff
. Leon Bankoff gave a copy of the manuscript to Professor Clayton Dodge of the University of Maine
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
, 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.
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, 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 AmericanScientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...
's "Mathematical Games" editor Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
. The manuscript was forwarded to Leon Bankoff
Leon Bankoff
Leon Bankoff , born in New York City, New York, was an American dentist and mathematician.- Life :...
. Leon Bankoff gave a copy of the manuscript to Professor Clayton Dodge of the University of Maine
University of Maine
The University of Maine is a public research university located in Orono, Maine, United States. The university was established in 1865 as a land grant college and is referred to as the flagship university of the University of Maine System...
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
Biola University is a private, evangelical Christian, liberal arts university located near Los Angeles. Biola's main campus is in La Mirada in Los Angeles County, California. In addition, the university has several satellite campuses in Chino Hills, Inglewood, San Diego, and Laguna Hills.-...
, 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
Woo circles
In geometry, the Woo circles, introduced by Peter Y. Woo, are a set of infinitely many Archimedean circles.-Construction:Form an arbelos with the two inner semicircles tangent at point C. Let m denote any nonnegative real number. Draw two circles, with radii m times the radius of the smaller two...
in 1999.
External links
- Online catalogue of Archimedean circles
- Hiroshi Okumura and Masayuki Watanabe (2004). "The Archimedean Circles of Schoch and Woo". Forum Geometricorum Volume 4.