ENGLISH

All Sides to an Oval: Properties, Parameters and Borromini's Mysterious Construction

By Angelo Alessandro Mazzotti

Book information

Publisher
Springer International Publishing
Year
2019
ISBN
978-3-030-28809-9, 978-3-030-28810-5
Language
english
Format
PDF
Filesize
9 MB (9332341 bytes)
Edition
2nd ed. 2019
Pages
XIII, 190\197
Time added
2020-02-08 04:41:45
Mathematics; Geometry; Mathematics in Art and Arch

Description

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. Front Matter ....Pages i-xiii Introduction (Angelo Alessandro Mazzotti)....Pages 1-4 Properties of a Polycentric Oval (Angelo Alessandro Mazzotti)....Pages 5-18 Ruler/Compass Constructions of Simple Ovals (Angelo Alessandro Mazzotti)....Pages 19-61 Parameter Formulas and Equations for Simple Ovals and Applications (Angelo Alessandro Mazzotti)....Pages 63-102 Optimisation Problems for Ovals (Angelo Alessandro Mazzotti)....Pages 103-109 Remarkable Four-Centre Oval Shapes (Angelo Alessandro Mazzotti)....Pages 111-127 Borromini’s Ovals in the Dome of San Carlo alle Quattro Fontane in Rome (Angelo Alessandro Mazzotti)....Pages 129-160 Ovals with 4n Centres: The Ground Plan of the Colosseum and the Neuilly Bridge Arches (Angelo Alessandro Mazzotti)....Pages 161-188 Back Matter ....Pages 189-190

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