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Perimeter Determination of the Eight-Centered Oval

  • Jean-Marc GinouxEmail author
  • Jean-Claude Golvin
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While the ellipse is a plane curve known since Greek antiquity, a precise expression for its perimeter was established only in the eighteenth century by means of an integral that can be calculated numerically by a series expansion. Previously, a number of approximations were proposed at various times to provide a formula for approximating this perimeter. Beginning in the sixteenth century, several authors showed that an oval with eight centers coincides almost perfectly with the ellipse constructed on the same axes and can be considered a representation of the latter, provided that the radii of the arcs of the circles that compose it have been suitably chosen. It follows that the computation of the ellipse’s perimeter is thereby reduced to a simple sum of lengths of arcs of circles. However, it does not appear to us that this calculation, which could prove useful for geometers as well as archeologists, has ever been performed or published. The purpose of this work is thus, on the one...

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Notes

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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Authors and Affiliations

  1. 1.Laboratoire LIS, CNRSUMR 7020 Université de ToulonLa Garde CedexFrance
  2. 2.Directeur de Recherches au CNRSUniversité de Bordeaux IIIMichel de MontaigneFrance

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