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2017 | OriginalPaper | Chapter

3. Ruler/Compass Constructions of Simple Ovals

Author : Angelo Alessandro Mazzotti

Published in: All Sides to an Oval

Publisher: Springer International Publishing

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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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previous chapter Properties of a Polycentric Oval
next chapter Parameter Formulas for Simple Ovals and Applications
Footnotes
1
Most of this section has already been published in the Nexus Network Journal (see [7])
 
2
This numbering differs from that in [7]
 
3
Most of this section has already been published in the Nexus Network Journal (see [7])
 
4
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)
 
5
Since a point does not come in the form of a parameter, we number this construction 117.
 
Literature
1.
Bosse, A.: Traité des Geometrales et Perspectives Enseignées dans l'Academie Royale de la Peinture et Sculpture. L’Auteur, Paris (1655)
2.
Curioni, G.: Geometria pratica applicata all’arte del costruttore. Torino (1877)
3.
Docci, M., Migliari, R.: Architettura e geometria nel Colosseo di Roma. In: Atti del Convegno (ed.) Matematica e architettura. Metodi analitici, metodi geometrici e rappresentazioni in architettura, Università di Firenze, Fac. Architettura, Firenze 13–15 gennaio 2000, pp. 13–24. Alinea Editrice, Firenze (2001)
4.
Donghi, D.: Il manuale dell’architetto. Torino (1925)
5.
Dotto, E.: Note sulle costruzioni degli ovali a quattro centri. Vecchie e nuove costruzioni dell’ovale. Disegnare Idee Immagini. XII(23), 7–14 (2001)
6.
Mazzotti, A.A.: A Euclidean approach to eggs and polycentric curves. Nexus Netw. J. 16(2), 345–387 (2014)CrossRefMATH
7.
Mazzotti, A.A.: What Borromini might have known about ovals. Ruler and compass constructions. Nexus Netw. J. 16(2), 389–415 (2014)CrossRefMATH
8.
Ragazzo, F.: Geometria delle figure ovoidali. Disegnare idee immagini. VI(11), 17–24 (1995)
9.
Tosca i Masco, T.V.: Compendio matemàtico: Que comprehende Arquitectura civil, montea, y canteria, arquitecura militar, pirotechnia. Tomo V. Por Antonio Bordazar, Valencia (1712)
Metadata
Title
Ruler/Compass Constructions of Simple Ovals
Author
Angelo Alessandro Mazzotti
Copyright Year
2017
Book
All Sides to an Oval

Print ISBN: 978-3-319-39374-2

Electronic ISBN: 978-3-319-39375-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-39375-9_3

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