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

ISBN-13: 9783030288099 / Angielski / Twarda / 2019 / 190 str.

Angelo Alessandro Mazzotti

Recenzje

"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)

Spis treści

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. 

O autorze

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.

Blurb

“The book is an original, interesting and opportune contribution to an area not contemplated in geometry courses.” (Mathematical Reviews Clippings)

 “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.” (Nexus Netw J)

 “We think that the reader, whatever his or her academic background, will enjoy the logical sequence of the reasoning, the drawings, and the clarity of language in this book.” (The Mathematical Intelligencer)

  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.