Maths is a game and
in every game there is Maths
Angelo is
MA in Mathematics
PhD in Operations Research
High School teacher
Game inventor
Training and final exam to be a Mathematics and Physics teacher in the Italian public education system.
Dottorato di Ricerca (PhD) in OPERATIONS RESEARCH.
Winner of a position as Mathematics teacher in high school having passed written and oral examinations.
Laurea (BAC+1) in MATHEMATICS, with final mark of 110/110 cum laude.
One year scholarship at the Department of Applied Mathematics and Statistics in Stony Brook as visiting student NY – USA.
10-month grant at the Istituto Nazionale di Alta Matematica (INDAM)
Published by Springer.
Published on Galileo – Online scientific journal.
Published by Springer.
Published in Nexus Network J. 16: 345-387.
Published in Nexus Network J. 16: 389-415.
With A.Carlini, M.C.Recchioni e F.Zirilli - on J.Math.Phys. 36.
PhD Thesis.
BA Thesis.
My formulas and procedures to draw ovals, eggs and a class of more general polycentric curves can be implemented in CAD software.
Properties, parameters and Borromini's mysterious construction. (2nd edition 2019, Springer Ed.)
A EUCLIDEAN APPROACH TO EGGS AND POLYCENTRIC CURVES
(2014, Nexus Network Journal, 10.1007/s00004-014-0189-5)
Abstract. I tackle here the problem of smoothly connecting two arcs of curves with two more arcs, and present the application of this procedure to the drawing of a class of egg-shaped curves and to the generation of some open and closed polycentric curves. I provide solid mathematical background as well as ruler and compass constructions, some of them new. The use of basic, although lengthy, Euclidean proof tools suggests these properties and techniques were within reach – if not known – by architects and scientists long before the invention of analytic geometry.
WHAT BORROMINI MIGHT HAVE KNOWN ABOUT OVALS. RULER AND COMPASS CONSTRUCTIONS
(2014, Nexus Network Journal, 10.1007/s00004-014-0190-z)
Abstract. This paper is about drawing ovals once a sufficient number of certain parameters is given. New constructions are displayed, including the case when the symmetry axes are not given. Many of these make use of a recent conjecture by Ragazzo, for which I found a Euclidean proof, thus suggesting it might have been known at the time Borromini chose the ovals for the dome of San Carlo alle Quattro Fontane.
My personal archive of oval constructions.
All constructions are justified by my own mathematical proofs (see the above cited paper).
Ovals of given axis lines, given three independent parameters:
Ovals 01 to 04: Constructing ovals with given axis lines – Ovals 01 02 03 and 04
Ovals 05 06 07 and 09: Constructing ovals with given axis lines – Ovals 05 06 07 and 09
Ovals 10 and 11a: Constructing ovals with given axis lines – Ovals 10 and 11a
Ovale 11b: Constructing ovals with given axis lines – Oval 11b
Ovals 12 14 15 and 16: Constructing ovals with given axis lines – Ovals 12 14 15 and 16
Ovals 17 to 20: Constructing ovals with given axis lines – Ovals 17 18 19 and 20
Ovals 21 to 23: Constructing ovals with given axis lines – Ovals 21 22 and 23
Oval with the minimum radius ratio: Oval with minimum ratio of the radii, for any given axis measures
The stadium problem: The stadium problem
Ovals of unknown axis lines, given six independent parameters.
Ovals 106 (U7) and 120 (U21): Ovals with unknown axis lines – Ovals 106 and 120
Ovals 121 (U22) and 122 (U23): Ovals with unknown axis lines – Ovals 121 and 122
Ovals 132 (U26) and 160 (U29): Ovals with unknown axis lines – Ovals 132 and 160
My personal archive of egg constructions.
All constructions are justified by my own mathematical proofs (see the above cited paper).
Construction of an egg given the same centres taken in a different order.
Construction of an egg inscribed inside a trepezium.
Construction of eggs: Constructing a six-centre egg from its centres or inscribing it inside a trapezoid
My personal archive of constructions of polycentric curves.
All constructions are justified by my own mathematical proofs (see the above cited paper).
Four-arc polycentric curves constructed starting from two external arcs.
Given two arcs and a point on each one of them I draw the Connection Locus, made of two circles. Choosing then a point on one or the other circle it is possble to draw two tangent circles. Any choice of four consecutive arcs yields a polycentric curve: Constructing a class of four-arc polycentric curves (PCCSs) by means of the Connection Locus (CL)
Four-arc closed polycentric curves, starting from two connection points and two tangents.
Drawing four-arc closed polycentric curves, starting from two connection points and two tangents, by means of the Connection Locus: Constructing a class of four-arc closed polycentric curves by means of the Connection Locus (CL)
ALL SIDES TO AN OVAL. Properties, Parameters and Borromini's mysterious Construction
“The book is an original, interesting and opportune contribution to an area not contemplated in geometry courses. “ (U. D'Ambrosio, Mathematical Reviews Clippings, April 2018)
“Angelo Mazzotti’s All Sides to an Oval addresses a fundamental subject for architects, civil engineers and mathematicians involved in designing oval forms or analysing existing ones. 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. In addition, the author poses some new geometrical constructions. A book of this kind on this subject was necessary since only some partial expositions have been previously published. All sections are illustrated with clear drawings that permit an easy understanding. Mazzotti’s training in mathematics and geometry gives him the best skills to carry out this work. [ ] 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 López-Mozo, book review in Nexus Netw J (2018) 20:303–304)
“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 written 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. Temesvari, zbMATH, 2017)
"Angelo Alessandro Mazzotti, professeur à ITC Di Vittorio à Rome, leur a consacré cette étude exhaustive, avec de très nombreuses figures et illustrationsè[...] Nous avons particulièrement apprécié le catalogue des ovales à quatre centres les plus remarquables, utilisés dans l’architecture aux XVIème et XVIIème siècles. Ce livre intéressera également les amateurs d’architecture classique car il comporte des descriptions très complètes des ovales de Borromée du dome de l’église Saint-Charles-aux-quatre-fontaines à Rome, ou encore des ovales figurant dans le plan du Colysée.” (from the book Fous de codes (Secrets) by Mark Frary, Flammerion Ed., 2018)