Skip to main content

Sets That Contain Their Circle Centers

Buy Article:

$12.00 plus tax (Refund Policy)

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.
No Reference information available - sign in for access.
No Citation information available - sign in for access.
No Supplementary Data.
No Data/Media
No Metrics

Document Type: Research Article

Publication date: 2008-11-01

More about this publication?
  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more