Properties of a Polycentric Oval

  • Angelo Alessandro Mazzotti


In this chapter we sum up the well-known properties of an oval and add new ones, in order to have the tools for the various constructions illustrated in Chap.  3 and for the formulas linking the different parameters, derived in Chap.  4. All properties are derived by means of mathematical proofs based on elementary geometry and illustrated with drawings.


  1. 1.
    Bosse, A.: Traité des Geometrales et Perspectives Enseignées dans l’Academie Royale de la Peinture et Sculpture. L’Auteur, Paris (1655)Google Scholar
  2. 2.
    Mazzotti, A.A.: A Euclidean approach to eggs and polycentric curves. Nexus Netw. J. 16(2), 345–387 (2014)CrossRefGoogle Scholar
  3. 3.
    Mazzotti, A.A.: What Borromini might have known about ovals. Ruler and compass constructions. Nexus Netw. J. 16(2), 389–415 (2014)CrossRefGoogle Scholar
  4. 4.
    Ragazzo, F.: Geometria delle figure ovoidali. Disegnare idee immagini. VI(11), 17–24 (1995)Google Scholar
  5. 5.
    Ragazzo, F.: Curve Policentriche. Sistemi di raccordo tra archi e rette. Prospettive, Roma (2011)Google Scholar
  6. 6.
    Rosin, P.L.: A survey and comparison of traditional piecewise circular approximations to the ellipse. Comput. Aided Geomet. Des. 16(4), 269–286 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Tweddle, I.: James Stirling: ‘This About Series and such Things’. Scottish Academic Press, Cambridge, UK (1988)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Angelo Alessandro Mazzotti
    • 1
  1. 1.RomaItaly

Personalised recommendations