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Most cited

This page lists all time most cited articles for this title. Please use the publication date filters on the left if you would like to restrict this list to recently published content, for example to articles published in the last three years. The number of times each article was cited is displayed to the right of its title and can be clicked to access a list of all titles this article has been cited by.

Contents

Page 114 of 187

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  • Triangles whose sides form an arithmetic progression

  • Sadi Abu-Saymeh, Mowaffaq Hajja
  • Published online by Cambridge University Press:
    08 October 2020, pp. 469-481

  • This article is motivated by, and is meant as a supplement to, the recent paper [1]. That paper proves three geometric characterisations of triangles whose sides are in arithmetic progression, or equivalently triangles in which one of the sides is the arithmetic mean of the other two. More precisely, it gives three geometric contexts in which such triangles appear. In this Article, we supply references for the results in [1] and we provide more proofs of these results. We also add more contexts in which such triangles appear, and we raise related issues for future work. We hope that this will be a source of problems for training for, and for including in, mathematical competitions.

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  • More power to Pascal

  • Barry Lewis
  • Published online by Cambridge University Press:
    01 August 2016, pp. 454-465

  • Pascal’s triangle is the most famous of all number arrays - full of patterns and surprises. One surprise is the fact that lurking amongst these binomial coefficients are the triangular and pyramidal numbers of ancient Greece, the combinatorial numbers which arose in the Hindu studies of arrangements and selections, together with the Fibonacci numbers from medieval Italy. New identities continue to be discovered, so much so that their publication frequently excites no one but the discoverer.

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Page 114 of 187