Abstract
Given 5 points in the plane, no 3 on a line, no 4 on a circle, there are 10 circles that contain 3 of those points. We are interested in those circles that separate the remaining 2 points, i.e. that leave one of these points in their interior and the other in their exterior. Such a circle will be called a point splitting circle, or simply a splitting circle.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
R. Honsberger. Mathematical Gems III. Dolciani Mathematical Expositions, 9: 18–19, 1985.
R. Honsberger. Mathematical Morsels, Problem 23. Dolciani Mathematical Expositions, 3: 48–51, 1978.
F. Swetz. The Chinese Mathematical Olympiads: a case study. The American Mathematical: Monthly, 79: 899–904, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Post, K.A. (1990). A Curious Property of Points and Circles in the Plane. In: Feijen, W.H.J., van Gasteren, A.J.M., Gries, D., Misra, J. (eds) Beauty Is Our Business. Texts and Monographs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4476-9_42
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4476-9_42
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8792-6
Online ISBN: 978-1-4612-4476-9
eBook Packages: Springer Book Archive