All Sides to an Oval

Properties, Parameters, and Borromini's Mysterious Construction

Authors: Mazzotti, Angelo Alessandro

  • Unprecedented and complete cover of the topic of polycentric ovals written in a highly readable style for a broad audience
  • Presents more than 30 constructions and corresponding links to animation videos
  • Contains a breakthrough study of the geometry of the dome of the church of San Carlo alle Quattro Fontane in Rome
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Buy this book

eBook 27,36 €
price for Spain (gross)
  • ISBN 978-3-319-39375-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 34,31 €
price for Spain (gross)
  • ISBN 978-3-319-39374-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This is the only book dedicated to the Geometry of Polycentric Ovals. It includes problem solving constructions and mathematical formulas. For anyone interested in drawing or recognizing an oval, this book gives all the necessary construction and calculation tools. More than 30 basic construction problems are solved, with references to Geogebra animation videos, plus the solution to the Frame Problem and solutions to the Stadium Problem.

A chapter (co-written with Margherita Caputo) is dedicated to totally new hypotheses on the project of Borromini’s oval dome of the church of San Carlo alle Quattro Fontane in Rome. Another one presents the case study of the Colosseum as an example of ovals with eight centres.

The book is unique and new in its kind: original contributions add up to about 60% of the whole book, the rest being taken from published literature (and mostly from other work by the same author).

The primary audience is: architects, graphic designers, industrial designers, architecture historians, civil engineers; moreover, the systematic way in which the book is organised could make it a companion to a textbook on descriptive geometry or on CAD.

About the authors

MA in Mathematics and PhD in Operations Research, Angelo A. Mazzotti has been a high school teacher for more than 20 years. In 2011 he went back to research studying Polycentric Curves and Ovals in particular, and started working as a freelance mathematician. Angelo is also a game inventor and a jazz singer.

Reviews

“The book contains a comprehensive collection of geometrical constructions and mathematical equations on the properties of ovals, the main parameters for managing them, and two case studies of actual built oval forms. … Angelo Mazzotti’s All Sides to an Oval is a fundamental book for anyone working with oval forms from the point of view of the geometric control of the shapes.” (Ana Lo´pez-Mozo,  Nexus Network Journal, Vol. 20 (1), April, 2018)

“Everything is clearly explained and the many illustrations produced with geogebra are crystal clear. It might however be interesting to have a look at the associated website www.mazzottiangelo.eu/en/pcc.asp where you find links to YouTube videos showing animated geogebra constructions. … For the mathematician, it is invaluable because it brings together so much information that was either not known or never writen down or if it was, then at least it was scattered in diverse publications” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, March, 2017)

“This interesting book deals with surprising properties of polycentric ovals and applications. … The text and the figures are very readable. The historical remarks and the fields of applications are interesting. The book is enjoyable not only for mathematicians.” (Agota H. Temesvári, zbMATH 1370.51001, 2017)


Table of contents (8 chapters)

  • Introduction

    Mazzotti, Angelo Alessandro

    Pages 1-4

    Preview Buy Chapter 30,19 €
  • Properties of a Polycentric Oval

    Mazzotti, Angelo Alessandro

    Pages 5-18

    Preview Buy Chapter 30,19 €
  • Ruler/Compass Constructions of Simple Ovals

    Mazzotti, Angelo Alessandro

    Pages 19-60

    Preview Buy Chapter 30,19 €
  • Parameter Formulas for Simple Ovals and Applications

    Mazzotti, Angelo Alessandro

    Pages 61-91

    Preview Buy Chapter 30,19 €
  • Optimisation Problems for Ovals

    Mazzotti, Angelo Alessandro

    Pages 93-99

    Preview Buy Chapter 30,19 €

Buy this book

eBook 27,36 €
price for Spain (gross)
  • ISBN 978-3-319-39375-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 34,31 €
price for Spain (gross)
  • ISBN 978-3-319-39374-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
All Sides to an Oval
Book Subtitle
Properties, Parameters, and Borromini's Mysterious Construction
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-39375-9
DOI
10.1007/978-3-319-39375-9
Hardcover ISBN
978-3-319-39374-2
Edition Number
1
Number of Pages
X, 160
Number of Illustrations and Tables
3 b/w illustrations, 126 illustrations in colour
Topics