All Sides to an Oval

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.

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.

"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 www.mazzottiangelo.eu/en/pcc.asp 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, euro-math-soc.eu, 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)