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A geometric proof of the binomial identity
Published online by Cambridge University Press: 12 November 2024
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We give a geometric proof of the binomial identity for all natural n and real a,b. This work was inspired by the book [1], where the binomial identity for n = 3 and a,b > 0 is proved by breaking a cube C of size (a + b) × (a + b) × (a + b) into eight rectangular boxes and counting their volumes as follows.
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- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association
References
Inclusion–exclusion principle, Wikipedia, accessed March 2024 at https://en.wikipedia.org/wiki/Inclusion-exclusionprincipleGoogle Scholar