Convex Figures and the Function S(F)

  • Alexander Soifer


A perfect result is achieved, a series of problems is solved. Now what?Well, a good solution to a good problemgeneratesmany new questions. That is why mathematics will always be alive!

We have found an interesting property of the triangle: in any set of five points in a triangle of area S there are three points that forma triangle of area at most S/4. Moreover, five is the minimal number of points in a triangle that guarantees this result.


Equilateral Triangle Maximum Area Supporting Line Parallel Projection Pigeonhole Principle 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.College of Letters, Arts and SciencesUniversity of Colorado at Colorado SpringsColorado SpringsUSA

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