Angelo A. Mazzotti

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

 

Highlights

ALL SIDES TO AN OVAL

Properties, parameters and Borromini's mysterious construction.

GAMMAGRAPHICS (website)

Founder and administrator of Gammagraphics.

POLYCENTRICS (website)

Inventor of Polycentrics.

My Resume

Education

Titles

  • Liceo Scientifico “Tullio Levi-Civita”

    June - Nov 2000

    Training and final exam to be a Mathematics and Physics teacher in the Italian public education system.

  • Università degli studi di Roma "La Sapienza"

    1990 – 1994

    Dottorato di Ricerca (PhD) in OPERATIONS RESEARCH.

  • 1992

    Winner of a position as Mathematics teacher in high school having passed written and oral examinations.

  • Università degli studi di Roma “La Sapienza”

    1984 – 1989

    Laurea (BAC+1) in MATHEMATICS, with final mark of 110/110 cum laude.

Grants and scholarships

  • State University of New York, USA

    1992-1993

    One year scholarship at the Department of Applied Mathematics and Statistics in Stony Brook as visiting student NY – USA.

  • Rome

    1990 – 1991

    10-month grant at the Istituto Nazionale di Alta Matematica (INDAM)

Work Experience as mathematician

  • Mathematics consulting for freelance professionals

  • Teaching of Mathematics and basic Computer Science skills (since 1999) and coordination of the project "Polisportiva Matematici" preparing students to participate in mathematics competitions (since 2009) at the school ITIS "Lattanzio" in Rome

  • Teaching of Mathematics and basic Computer Science skills at the school IPSIA "T.Minniti" in Guidonia (1993 - 1999)

  • Private lessons in Mathematics for university and high school students

Written and published material

  • All Sides to an Oval. Properties, Parameters and Borromini's Mysterious Construction. 2nd edition

    2019

    Published by Springer.

  • L'emancipazione dell'ovale.

    Aug 1st 2017

    Published on Galileo – Online scientific journal.

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

    2017

    Published by Springer.

  • A Euclidean approach to eggs and polycentric curves.

    2014

    Published in Nexus Network J. 16: 345-387.

  • What Borromini might have known about ovals. Ruler and compass constructions.

    2014

    Published in Nexus Network J. 16: 389-415.

  • Asymptotic eigenvalue degeneracy for a class of three-dimensional Fokker-Planck operators.

    1995

    With A.Carlini, M.C.Recchioni e F.Zirilli - on J.Math.Phys. 36.

  • Processi di diffusione riflessi e ottimizzazione globale in un dominio.

    1994

    PhD Thesis.

  • L’uso dei metodi per la ottimizzazione nonlineare nel problema della programmazione lineare.

    1989

    BA Thesis.

Games and puzzles

  • Creation of the table game Contatto!
  • Invention of a Game Application called Polycentrics (patented) for smartphones and tablets (in progress).
  • Creation of the table game Il Filmimo on films (patented), together with Luciano Benvenuto (for the prototype) and Annalisa De Rose (for the marketing).
  • Creation of crossword puzzles and other puzzles for private use.
  • Invention of a way of playing the card game Buraco as a tournament for 5 or 6 players.
  • Organisation of tournaments.
  • Invention of a Rome-based board for the game Risk! (prototype by Andrea Lupi).
  • Contribution to the marketing of the table game Il Grande Gioco del Golf by Luciano Benvenuto, together with Luisa d'Agostino and Annalisa De Rose.
  • Coordination for the Di Vittorio–Lattanzio school of the student mathematics games Olimpiadi della Matematica and Kangourou della Matematica.

Personal Competences

Languages

  • Italian (mother tongue)
  • English (excellent) – C2 certificate
  • German (very good) – C1 certificate
  • French (good) – eight-year course in public school

Artistic (see also www.angelomazzotti.eu)

  • Jazz singing since 2005 (Scuola Popolare di Musica di Testaccio). Classes, workshops, concerts in Italy and in Germany (Berlin)
  • Writing of songs or just lyrics in Italian, English and German (since 2008).
  • Choir singing since 1983 (CIMA, AMPEM, Todavìa Canta, Sacri Montis, TJazzVoices, Fleeting Glance and ANKA Vocal Band choirs)
  • Pop and rock singing since 1985 (concerts in Rome with Penta and Tonic band)
  • Folk guitar and singing since 1983 (self-taught). Concerts in Rome and in Germany
  • Basic level of piano (SPMT), harmonica, electric bass, percussions.
  • Dancing, coreographing and teaching of Tango Argentino from 1996 (studied mainly at the Centro del Tango Argentino “Astor Piazzolla” in Rome). National-TV shows and theatre shows.
  • Direction and writing of a theatre musical (Un suono da marciapiede in 1992 at the Teatro de’ Servi in Rome)
  • Workshops and/or classes of: acting, modern dancing, circus, swing dance and salsa dance

Computer

  • Good level: Geogebra, spreadsheets, word processing, music writing software, search motors
  • Basic level: image and audio processing
  • Basic level programming: Basic, Fortran, Simscript, Pascal, C++

Organisation and social competences

  • Accustomed to working in groups and to collaborating
  • Organising groups and communicating

Ovals and Polycentric Curves

My formulas and procedures to draw ovals, eggs and a class of more general polycentric curves can be implemented in CAD software.

ALL SIDES TO AN OVAL

Properties, parameters and Borromini's mysterious construction. (2nd edition 2019, Springer Ed.)

PAPERS PUBLISHED IN THE NEXUS NETWORK JOURNAL:


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.

Constructing ovals – Geogebra animation videos

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:

 

  • Oval 01 – given the measure of the axes and the centre of the smaller circumference.
  • Oval 02 – given the measure of the axes and the distance of the connecting point from the minor axis.
  • Oval 03 - given the measure of the axes and the centre of the bigger circumference.
  • Oval 04 - given the measure of the axes and the distance of the junction point from the major axis.

Ovals 01 to 04: Constructing ovals with given axis lines – Ovals 01 02 03 and 04

  • Oval 05 - given the measure of the major axis, the centre of the smaller circumference and the distance of the junction point from the minor axis.
  • Oval 06 - given the measure of the major axis and the two centres of the circumferences.
  • Oval 07 - given the measure of the major axis, the centre of the smaller circumference and the distance of the junction point from the major axis.
  • Oval 09 - given the measure of the minor axis and the two centres of the circumferences.

Ovals 05 06 07 and 09: Constructing ovals with given axis lines – Ovals 05 06 07 and 09

  • Oval 10 - given the measure of the major axis, the centre of the bigger circle and the distance of the connection point to the major axis.
  • Oval 11a - given the measure of the minor axis, the centre of the smaller circle and the distance of the connection point to the minor axis.

Ovals 10 and 11a: Constructing ovals with given axis lines – Ovals 10 and 11a

  • Oval 11b - given the measure of the minor axis, the centre of the smaller circle and the distance of the connection point to the minor axis. SECOND CONSTRUCTION.

Ovale 11b: Constructing ovals with given axis lines – Oval 11b

  • Oval 12 - given the measure of the minor axis and the two centres of the circumferences.
  • Oval 14 - given the measure of the minor axis, the centre of the big circumference and the distance of the junction point from the minor axis.
  • Oval 15 - given the minor axis and the distances of the connection point from the two axis.
  • Oval 16 - given the minor axis, the centre of the bigger circumference and the distance of the connection point from the major axis.

Ovals 12 14 15 and 16: Constructing ovals with given axis lines – Ovals 12 14 15 and 16

  • Oval 17 - given the centres of the two circumferences and the distance of the connection point from the minor axis.
  • Oval 18 - given the centre of the smaller circumference and the distances of the connection point from the two axes.
  • Oval 19 - given the centres of the two circumferences and the distance of the connection point from the major axis.
  • Oval 20 - given the centre of the bigger circumference and the distance of the connection point from the two axes.

Ovals 17 to 20: Constructing ovals with given axis lines – Ovals 17 18 19 and 20

  • Oval 21 – given the two axes and the angle of the line of the centres.
  • Oval 22 - given the centers of the two circumferences and the ratio between the two axes.
  • Oval 23 - given the centre of the small circumference and the radii of both circumferences.

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.

  • Oval 106 (U7) of unknown axis lines – given the two vertices on the major axis, the distance of the centre of one of the smaller circumferences to the minor axis and the distance of the connection point to the major axis
  • Oval 120 (U21) of unknown axis lines - given two consecutive vertices, the (constrained) connection point and the (constrained) centre of simmetry.

Ovals 106 (U7) and 120 (U21): Ovals with unknown axis lines – Ovals 106 and 120

  • Oval 121 (U22) of unknown axis lines – given two consecutive vertices and the centre of the smaller circumference.
  • Oval 122 (U23) of unknown axis lines – given two consecutive vertices and the centre of the bigger circumference.

Ovals 121 (U22) and 122 (U23): Ovals with unknown axis lines – Ovals 121 and 122

  • Oval 132 (U26) of unknown axis lines - given two centres of consecutive circumferences, their (constrained) connection point and the (constrained) centre of simmetry.
  • Oval 160 (U29) of unknown axis lines - given a vertex on the major axis, its centre and a point on the same half oval along with a tangent through it.

Ovals 132 (U26) and 160 (U29): Ovals with unknown axis lines – Ovals 132 and 160

Construction of an egg given four independent centres.

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

Constructing certain PCCs – Geogebra animation videos

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)

Reviews

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)

Contact

  • Phone (it): 0039 339 4940 558
  • Phone (de): 0049 176 7609 6794
  • Email : angelomazzotti@gmail.com

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