Overview

This is the second edition of 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, representation  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 as well as the case study of Perronet’s Neuilly bridge, a half oval with eleven centres. 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. Added features in the 2nd edition include: the revised hypothesis on Borromini’s project for the dome of the church of San Carlo alle Quattro Fontane in Rome, an insight into the problem of finding a single equation to represent a four-centre oval, a suggestion for a representation of a four-centre oval using Geogebra, formulas for parameters of ovals with more than 4 centres and the case study of the eleven-centre half-oval arch used to build the XVIII century Neuilly bridge in Paris.

Full Product Details

Author:   Angelo Alessandro Mazzotti
Publisher:   Springer Nature Switzerland AG
Imprint:   Springer Nature Switzerland AG
Edition:   2nd ed. 2019
Weight:   0.545kg
ISBN:  

9783030288099

ISBN 10:   3030288099
Pages:   190
Publication Date:   21 November 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface to the 2nd edition.-Introduction.-Properties of a polycentric oval.-Four Centre Ovals.- Ruler/Compass constructions of simple ovals.- Ovals with given symmetry axis lines.- Ovals with unknown axis lines.-Inscribing and circumscribing ovals – The frame problem.- The stadium problem and the running track.- Parameter formulas for simple ovals and applications.- Parameter formulas for simple ovals.- Limitations for the frame problem.- Measuring a four-centre oval.- Concentric Ovals - Possible Equations and Geogebra Representations of an Oval.-Optimisation problems for ovals.- Ovals with 4n centres.- Remarkable four-centre ovals .- Borromini's Ovals in the Dome of San Carlo alle Quattro Fontane in Rome.-Ovals with 4n Centres: the Ground Plan of the Colosseum and the Neuilly Bridge Arches.-Appendix.-References.-Acknowledgements. 

Reviews

The book is well documented. Each chapter contains numerous references and citations. There are numerous pictures throughout the text, as is to be expected, and the formulae need only high school algebra and trigonometry. (Michele Intermont, MAA Reviews, December 27, 2021)

“The book is well documented. Each chapter contains numerous references and citations. There are numerous pictures throughout the text, as is to be expected, and the formulae need only high school algebra and trigonometry.” (Michele Intermont, MAA Reviews, December 27, 2021)

Author Information

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.

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