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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 109 of 185

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  • Pansymmetrical Pencils

  • B.M. Peek
  • Published online by Cambridge University Press:
    03 November 2016, pp. 19-22

  • In Fig. 1, AA1A2A3 … is a rectangular hyperbola, whose asymptotes are OT, OT', and whose vertex is A. We make the following construction

    At A1, a point on the hyperbola, a tangent is drawn, cutting OA at P The tangent at A is drawn, cutting OA1 at P1. Let the other tangent from P1 touch the hyperbola at A2. Produce PA1 to cut OA2 at P2. Let the other tangent from P2 touch the hyperbola at A3, and let P1A2 produced cut OA3 at P3.

    Consider this process to be continued indefinitely and to be repeated on the other side of the axis OA, A′1 being the point of contact of the other tangent from P We obtain a pencil of rays OAn, OA′n which gradually lie closer together, becoming infinite in number as the asymptotes, which are the ultimate rays of the pencil, are approached. The system is obviously symmetrical about OA, and I shall show that this pencil has further remarkable properties, which I have named “pansymmetry” These properties can be stated thus

    If a tangent to the hyperbola at the point An be produced both ways, it will be symmetrically divided by all the rays of the pencil, the p th section on the one side of An being equal to the p th section on the other side.

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  • The mathematics of walking

  • R. B. Anderton
  • Published online by Cambridge University Press:
    01 August 2016, pp. 194-197

  • Since ‘a body continues in its state of rest or of uniform motion in a straight line except in so far as it is compelled by forces to change that state’, the very first question that should be asked about walking is why any energy at all need be expended in maintaining fixed speed on level ground. With a wheeled vehicle remarkably little force is exerted for this once it is got going, and virtually all the energy is used to overcome resistive drag. But the body is not dragged, and there is little resistance presented by relaxed, healthy limbs.

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  • The Mathematics of Borrowing Money

  • Fergus J. Gaines
  • Published online by Cambridge University Press:
    01 August 2016, pp. 14-18

  • Many people have had the experience of borrowing a sum of money which is to be repaid with interest by making equal monthly payments over a year or a number of years. Two problems suggest themselves:

    1. If the annual rate of interest is known what is the value of each monthly payment?

    2. If the monthly payment is known, what is the annual rate of interest?

Page 109 of 185