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A geometric interpretation of equal sums of cubes

Published online by Cambridge University Press:  01 August 2016

Adam Bailey
Adam Bailey*
Affiliation:
68 Robinson Road, Colliers Wood, London SW17 9DW, e-mail: e-mail: [email protected]
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Extract

Is there a three-dimensional equivalent of the Pythagorean theorem? It all depends, of course, what one means by equivalent. There are in fact several distinct results which can with some justice be regarded as threedimensional equivalents of the theorem.

One interpretation of the Pythagorean theorem is as a statement about any rectangle, expressing the square of its diagonal as the sum of the squares of its height and length. This readily extends to the case of a rectangular box (cuboid), for which the square of its long diagonal always equals the sum of the squares of its height, length and depth.

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 523 , March 2008 , pp. 8 - 13
Copyright
Copyright © The Mathematical Association 2008

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References

1. http://en.wikipedia.org/wiki/Jean_Paul_de_Gua_de_Malves Google Scholar
2. http://mathworld.wolfram.com/deGuasTheorem.html Google Scholar
3. Perfect, H., Pythagoras in higher dimensions, Math. Gaz. 62 (October 1978) p. 208 (also reprinted in [5]).Google Scholar
4. Hoehn, L., A neglected Pythagorean-like formula, Math. Gaz. 84 (March 2000) pp. 71–73 (also reprinted in [5]).Google Scholar
5. Pritchard, C. (ed.), The changing shape of geometry, Cambridge University Press (2003).Google Scholar