All Sides to an Oval
Properties, Parameters and Borromini's Mysterious Construction
Authors: Mazzotti, Angelo Alessandro
Free Preview- 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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- About this book
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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.
- About the authors
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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.
- Table of contents (8 chapters)
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Introduction
Pages 1-4
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Properties of a Polycentric Oval
Pages 5-18
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Ruler/Compass Constructions of Simple Ovals
Pages 19-61
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Parameter Formulas and Equations for Simple Ovals and Applications
Pages 63-102
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Optimisation Problems for Ovals
Pages 103-109
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- All Sides to an Oval
- Book Subtitle
- Properties, Parameters and Borromini's Mysterious Construction
- Authors
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- Angelo Alessandro Mazzotti
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-28810-5
- DOI
- 10.1007/978-3-030-28810-5
- Hardcover ISBN
- 978-3-030-28809-9
- Edition Number
- 2
- Number of Pages
- XIII, 190
- Number of Illustrations
- 5 b/w illustrations, 149 illustrations in colour
- Topics
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