© 2017

All Sides to an Oval

Properties, Parameters, and Borromini's Mysterious Construction


Table of contents

  1. Front Matter
    Pages i-x
  2. Angelo Alessandro Mazzotti
    Pages 1-4
  3. Angelo Alessandro Mazzotti
    Pages 5-18
  4. Angelo Alessandro Mazzotti
    Pages 19-60
  5. Angelo Alessandro Mazzotti
    Pages 61-91
  6. Angelo Alessandro Mazzotti
    Pages 93-99
  7. Angelo Alessandro Mazzotti
    Pages 101-115
  8. Angelo Alessandro Mazzotti
    Pages 145-158
  9. Back Matter
    Pages 159-160

About this book


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.


51E21,00A67. ovals polycentric curves ruler/compass constructions stadiums Geogebra

Authors and affiliations

  1. 1.Istituto di Istruzione Superiore“I.T.C. Di Vittorio – I.T.I. Lattanzio”RomaItaly

About the authors

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.

Bibliographic information


“The work is complete and articulate, placing the most exquisitely mathematical and geometric aspects—which identify the construction of the ovals in relation to the parameters that define them—alongside aesthetic and architectural ones. … 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.” (Roberta Spallone and Marco Vitali, The Mathematical Intelligencer, Vol. 41, 2019)

“The book contains a comprehensive collection of geometrical constructions and mathematical equations on the properties of ovals, the main parameters for managing them, and two case studies of actual built oval forms. … 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.” (Ana Lo´pez-Mozo,  Nexus Network Journal, Vol. 20 (1), April, 2018)

“Everything is clearly explained and the many illustrations produced with geogebra are crystal clear. It might however be interesting to have a look at the associated website where you find links to YouTube videos showing animated geogebra constructions. … For the mathematician, it is invaluable because it brings together so much information that was either not known or never writen down or if it was, then at least it was scattered in diverse publications” (Adhemar Bultheel, European Mathematical Society,, March, 2017)

“This interesting book deals with surprising properties of polycentric ovals and applications. … The text and the figures are very readable. The historical remarks and the fields of applications are interesting. The book is enjoyable not only for mathematicians.” (Agota H. Temesvári, zbMATH 1370.51001, 2017)