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A generalization of Apollonius’ theorem

Published online by Cambridge University Press:  22 September 2016

A. J. Douglas
A. J. Douglas*
Affiliation:
Dept. of Pure Mathematics, The University of Sheffield
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Extract

It follows at once from Pythagoras’ theorem about a right-angled triangle that the sum of the squares of the lengths of the diagonals of a rectangle is equal to the sum of the squares of the lengths of the four sides. Apollonius showed that the assertion holds for a parallelogram and, more recently, Amir-Moez and Hamilton gave a generalization to quadrilaterals by introducing a correction term which depends on the distance between the mid-points of the diagonals.

Type
Research Article
Information
The Mathematical Gazette , Volume 65 , Issue 431 , March 1981 , pp. 19 - 22
Copyright
Copyright © Mathematical Association 1981

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References

1. Arair-Moez, Ali R. and Hamilton, J. D., A generalized parallelogram law, Maths. Mag. 49, 88–89 (1976).CrossRefGoogle Scholar