Skip to main content

2017 | OriginalPaper | Buchkapitel

3. Ruler/Compass Constructions of Simple Ovals

verfasst von : Angelo Alessandro Mazzotti

Erschienen in: All Sides to an Oval

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
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.
 
Literatur
1.
Zurück zum Zitat Bosse, A.: Traité des Geometrales et Perspectives Enseignées dans l'Academie Royale de la Peinture et Sculpture. L’Auteur, Paris (1655) Bosse, A.: Traité des Geometrales et Perspectives Enseignées dans l'Academie Royale de la Peinture et Sculpture. L’Auteur, Paris (1655)
2.
Zurück zum Zitat Curioni, G.: Geometria pratica applicata all’arte del costruttore. Torino (1877) Curioni, G.: Geometria pratica applicata all’arte del costruttore. Torino (1877)
3.
Zurück zum Zitat 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) 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.
Zurück zum Zitat Donghi, D.: Il manuale dell’architetto. Torino (1925) Donghi, D.: Il manuale dell’architetto. Torino (1925)
5.
Zurück zum Zitat Dotto, E.: Note sulle costruzioni degli ovali a quattro centri. Vecchie e nuove costruzioni dell’ovale. Disegnare Idee Immagini. XII(23), 7–14 (2001) 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.
Zurück zum Zitat Mazzotti, A.A.: A Euclidean approach to eggs and polycentric curves. Nexus Netw. J. 16(2), 345–387 (2014)CrossRefMATH Mazzotti, A.A.: A Euclidean approach to eggs and polycentric curves. Nexus Netw. J. 16(2), 345–387 (2014)CrossRefMATH
7.
Zurück zum Zitat Mazzotti, A.A.: What Borromini might have known about ovals. Ruler and compass constructions. Nexus Netw. J. 16(2), 389–415 (2014)CrossRefMATH Mazzotti, A.A.: What Borromini might have known about ovals. Ruler and compass constructions. Nexus Netw. J. 16(2), 389–415 (2014)CrossRefMATH
8.
Zurück zum Zitat Ragazzo, F.: Geometria delle figure ovoidali. Disegnare idee immagini. VI(11), 17–24 (1995) Ragazzo, F.: Geometria delle figure ovoidali. Disegnare idee immagini. VI(11), 17–24 (1995)
9.
Zurück zum Zitat Tosca i Masco, T.V.: Compendio matemàtico: Que comprehende Arquitectura civil, montea, y canteria, arquitecura militar, pirotechnia. Tomo V. Por Antonio Bordazar, Valencia (1712) Tosca i Masco, T.V.: Compendio matemàtico: Que comprehende Arquitectura civil, montea, y canteria, arquitecura militar, pirotechnia. Tomo V. Por Antonio Bordazar, Valencia (1712)
Metadaten
Titel
Ruler/Compass Constructions of Simple Ovals
verfasst von
Angelo Alessandro Mazzotti
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-39375-9_3