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On 3N points in a plane

Published online by Cambridge University Press:  24 October 2008

B. J. Birch
B. J. Birch
Affiliation:
Trinity College Cambridge
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Extract

In this note I prove the following theorem:

Theorem 1. Given 3N points in a plane, we can divide them into N triads such that, when we form a triangle with the points of each triad, the N triangles will all have a common point.

The proof depends on three lemmas; the first two are well known, and are quoted without proof; the third I believe to be new, and leads directly to the proof of the theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 4 , October 1959 , pp. 289 - 293
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

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