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Combinatorics: Ancient and Modern$
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Robin Wilson and John J. Watkins

Print publication date: 2013

Print ISBN-13: 9780199656592

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199656592.001.0001

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The arithmetical triangle

The arithmetical triangle

(p.167) Chapter 7 The arithmetical triangle
Combinatorics: Ancient and Modern


Oxford University Press

The arithmetical triangle is the most famous of all number patterns. Apparently a simple listing of the binomial coefficients, it contains the triangular and pyramidal numbers of ancient Greece, the combinatorial numbers that arose in the Hindu studies of arrangements and selections, and (barely concealed) the Fibonacci numbers from medieval Italy. It reveals patterns that delight the eye, raises questions that tax the number-theorists, and amongst the ‘… coefficients, there are so many relations present that when someone finds a new identity, there aren’t many people who get excited about it any more, except the discoverer!’

Keywords:   arithmetical triangle, binomial, triangular numbers, pyramidal numbers, Fibonacci numbers

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