Advertisement

Parameter Formulas and Equations for Simple Ovals and Applications

  • Angelo Alessandro Mazzotti
Chapter

Abstract

Many tools for drawing a polycentric oval subject to geometrical or aesthetical constraints have been presented in Chap.  3. In this chapter we derive formulas which on the other hand allow to calculate all important parameters when the value of three independent ones is known, as well as the limitations the given parameters are subject to. These formulas allow for a deeper insight in the properties of any oval, as will be shown on the chosen forms of Chap.  6. Cases included are numbered consistently with the construction numbers of Chap.  3. Also included is the proof of the formulas yielding the solution to the frame problem presented in Sect.  3.3 as well as formulas for the length of an oval and for the area surrounded by it. Section  4.4 is devoted to concentric ovals and their properties. Finally in Sect. 4.5 we tackle the problem of finding a closed form for the equation of a simple oval, and suggest a way of representing a generic one by means of Geogebra.

References

  1. 1.
    Dotto, E.: Note sulle costruzioni degli ovali a quattro centri. Vecchie e nuove costruzioni dell’ovale. Disegnare Idee Immagini. XII(23), 7–14 (2001)Google Scholar
  2. 2.
    López Mozo, A.: Oval for any given proportion in architecture: a layout possibly known in the sixteenth century. Nexus Netw. J. 13(3), 569–597 (2011)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.
    Rosin, P.L.: A family of constructions of approximate ellipses. Int. J. Shape Model. 8(2), 193–199 (1999)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Angelo Alessandro Mazzotti
    • 1
  1. 1.RomaItaly

Personalised recommendations