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Ruler/Compass Constructions of Simple Ovals

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All Sides to an Oval

Abstract

We can now show how most ovals can be drawn with ruler and compass if enough parameters are known. And after having mastered the basic ones, one is ready to tackle more complicated problems, such as the two Frame Problems or the Stadium Problem, which we will discuss in the second part of this chapter. All the following constructions have been made with freeware Geogebra and most of them are linked through the website www.mazzottiangelo.eu/en/pcc.asp, as described further. The much used Connection Locus—the CL—has just been defined in Chap. 2. All constructions in this chapter are general purpose constructions, in the sense that any combination of parameters, constrained within some values, can be chosen. Further combinations of parameters then those illustrated here are listed in the Appendix, for the reader to try out and find the corresponding constructions. Selected oval forms will then be presented in Chap. 6.

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Notes

  1. 1.

    This numbering differs from that in [7]

  2. 2.

    Again the numbering differs from that in [7]: the letter U has been added and 99 has been subtracted (e.g. Oval 105 has become Construction U6)

  3. 3.

    Since a point does not come in the form of a parameter, we number this construction 117.

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Mazzotti, A.A. (2017). Ruler/Compass Constructions of Simple Ovals. In: All Sides to an Oval. Springer, Cham. https://doi.org/10.1007/978-3-319-39375-9_3

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