Abstract
The proof technique “double counting” is presented. It is applied to computing sums of successive natural numbers. Vandermonde’s identity is introduced as an application. Golomb’s proof of Fermat’s little theorem using the counting of orbits is given. The number of edges of an icosahedron is computed using this technique. Pythagoras’s theorem is proven using equal areas.
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© 2015 Springer International Publishing Switzerland
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Joshi, M. (2015). Double Counting. In: Proof Patterns. Springer, Cham. https://doi.org/10.1007/978-3-319-16250-8_2
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DOI: https://doi.org/10.1007/978-3-319-16250-8_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16249-2
Online ISBN: 978-3-319-16250-8
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