Angelo Alessandro Mazzotti

All Sides to an Oval (eBook, PDF)

Properties, Parameters, and Borromini's Mysterious Construction

• Format: PDF

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer International Publishing
• Erscheinungstermin: 28. Februar 2017
• Englisch
• ISBN-13: 9783319393759
• Artikelnr.: 53031727

Autorenporträt

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.

Inhaltsangabe

Introduction.- Properties of a polycentric oval.-F .- 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.- Optimisation problems for ovals.- Ovals with 4n centres.- Remarkable four-centre ovals .-Appendix.-References.-Acknowledgements.

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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.

Rezensionen

"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)