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ERIC Number: EJ855795
Record Type: Journal
Publication Date: 2008-Nov
Pages: 10
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0746-8342
Sets that Contain Their Circle Centers
Martin, Greg
College Mathematics Journal, v39 n5 p357-366 Nov 2008
Say that a subset S of the plane is a "circle-center set" if S is not a subset of a line, and whenever we choose three non-collinear points from S, the center of the circle through those three points is also an element of S. A problem appearing on the Macalester College Problem of the Week website stated that a finite set of points in the plane, no three lying on a common line, cannot be a circle-center set. Various solutions to this problem that did not use the full strength of the hypotheses appeared, and the conjecture was subsequently made that every circle-center set is unbounded. In this article, we show how to prove a stronger assertion, namely that the one closed circle-center set is the entire plane, or equivalently that every circle-center set is dense in the plane. The step-by-step journey proceeds using elementary geometry for the most part, with a dash of plane topology thrown in.
Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A