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Perimeter Determination of the Eight-Centered Oval

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Notes

  1. See Y. Guillaumin [18, p. 72].

  2. “I found the oval that forms the wall ... for that I separated the perimeter into several arcs that I found to be able to be drawn with the compass by eight centers.” (see Figure 2).

  3. “Not only that, in fact, there are infinitely many combinations for the minor radius (\(R_1\)) and the major radius (\(R_3\)), as in the case of the oval with four centers, but there are also infinitely many possibilities of choice for the intermediate radius (\(R_2\)).”

  4. In a paper published by Robert M. Milne [30] in 1903, i.e., a few years before, one can read that

    Huygens published his approximation in 1654 in his “De Circuli Magnitudine Inventa” in the following form: “Any arc less than a semicircle is greater than its subtense together with one third of the difference, by which the subtense exceeds the sine, and less than the subtense together with a quantity, which is to the said third, as four times the subtense added to the sine is to twice the subtense with three times the sine.”

    .

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Acknowledgments

The authors would like to thank the reviewers for their helpful advice, which enabled us to greatly improve this work.

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  1. Laboratoire LIS, CNRS, UMR 7020 Université de Toulon, BP 20132, 83957, La Garde Cedex, France

    Jean-Marc Ginoux

  2. Directeur de Recherches au CNRS, Université de Bordeaux III, Michel de Montaigne, France

    Jean-Claude Golvin

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Ginoux, JM., Golvin, JC. Perimeter Determination of the Eight-Centered Oval. Math Intelligencer 42, 20–29 (2020). https://doi.org/10.1007/s00283-019-09946-z

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