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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 163 of 187

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  • Thoughts on a conjecture of Erdős

  • Stan Dolan
  • Published online by Cambridge University Press:
    16 October 2017, pp. 449-457

  • If two squares with no interior point in common are drawn inside a unit square then prove that the sum of their side-lengths is at most 1.

    This problem was posed in the 1930s by Paul Erdős [1]. It is the simplest case of a still unsolved conjecture.

    If k2 + 1 squares with no interior point in common are drawn inside a unit square then the maximum possible sum of their side-lengths is k [2].

    We shall use the notation S(n) to denote the maximum possible sum of the side-lengths for n squares drawn with no interior point in common inside a unit square. The main aim of this article will be to develop an approach to the study of the function S which will give surprisingly simple proofs of a number of known results. This approach will then be used to prove a new result about the asymptotic behaviour of S.

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  • A new look at functions in modular arithmetic

  • Marion H. Bird
  • Published online by Cambridge University Press:
    22 September 2016, pp. 78-86

  • When a function in arithmetic modulo n is represented through a cartesian graph, the resulting set of points reveals little information about the form of the function (for example, see Fig. 1). It is not easy to discern connections between the points; a restriction to the values 0, 1, 2,…, n — 1 would have to be placed on x and y; and the fact that n — 1 is as ‘near’ to 0 as 1 is, is not apparent in the graph.

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Page 163 of 187