As recreational mathematicians, we investigate a variety of topics.
The didactical projects also vary considerably because they stem from original ideas.
For the Visual Mathematics Dictionary and other "didactical material for all" by Antonella Perucca and collaborators, please see the dedicated webpage.
Publications
- Original proof of the Chinese Remainder Theorem: Antonella Perucca (Professor), The Chinese Remainder Clock, College Journal of Mathematics, vol. 48, no. 2, March 2017, 82-89, link.
- Understanding Knuth's algorithm for winning Mastermind: Tom Fiore (Postdoc), Alexandre Lang (Master student), and Antonella Perucca Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind, College Journal of Mathematics, vol. 49, no. 4, March 2018, link. See also: The Master Mind wheel and slides.
- Variants of the mathematical induction: Antonella Perucca and Milko Todorovic (Master student), Visualizations for the Principle of Mathematical Induction, link, Beiträge zum Mathematikunterricht 2020, WTM-Verlag Münster, 705–708. See also: slides.
- Plimpton 322: Antonella Perucca and Deborah Stranen (Master student), Converting the Old Babylonian Tablet ‘Plimpton 322’ into the Decimal System as a Classroom Exercise, link, Convergence, October 2020. See also: slides.
- Sliding mask for recurrence sequences: Antonella Perucca, Unmasking Recurrence Sequence,
link, Pi in the Sky, vol. 21, 2019.
- Multisets in arithmetics: Antonella Perucca, Multimengen für die Arithmetik, Beiträge zum Mathematikunterricht 2019, WTM-Verlag Münster, 613–616, link, see also Multisets in arithmetics, link.
- New proof of a classical result: Miguel Acosta (Postdoc) and Jean-Marc Schlenker (Professor), A hyperbolic proof of Pascal's Theorem, The Mathematical Intelligencer, vol. 43, no. 2, 2021, 130-133.link.
- Closed paths for arithmetic billiards: Antonella Perucca, Joe Reguengo De Sousa (Bachelor student) and Sebastiano Tronto (PhD student), Arithmetic billiards, Recreational Mathematics Magazine, vol. 9, no. 16, June 2022, 43-54, link.
- Multiplication tables: Antonella Perucca, The Easy Multiplication Tables, Poster, online material of the GDM Conference 2021, link.
- Reflecting around proportions: Antonella Perucca and Pit Ronk, Beware Proportions, link and PROPORTIONATE, link (prototype for an user-friendly proportion calculator), with an extract, link published in the online GDM Meeting 2022 Proceedings.
- New geometry theorems: Antonella Perucca and Emiliano Torti (Postdoc), Congruence Theorems for convex polygons involving sides, angles, and diagonals, International Journal of Geometry, vol. 12, no. 1, 2023, 83-92, link.
- On the planar configurations of Rubik Snakes: Francesco Grotto (Postdoc), Antonella Perucca and Tatjana Van Steenbergen Bergeron (High-school pupil), Rubik Snakes on a plane, to appear in the College Mathematical Journal.
- Graph theory meets arithmetics: Antonella Perucca, Tim Seuré (Master student) and Vincent Wolff (PhD student), Divisibility Graphs and Modular Multiplication Tables, American Mathematical Monthly, published online in 2024.
- Multilinguism: Antonella Perucca, Visual Mathematics Dictionary, GDM Mitteilungen, 2022, link.
- Sharing mental calculations: Rich Andrusiak (Professor) and Antonella Perucca, Parallel Computing and the Value of Teamwork, to appear in Mathematics Teacher: Learning and Teaching Pre-K-12.
- School reality: Antonella Perucca, Multiplying mathematical teachers, GDM Mitteilungen, 2023, link.
- School reality: Antonella Perucca, Soft skills for mathematical teachers, GDM Mitteilungen, 2023, link.
- Understanding Congruence Theorems: Antonella Perucca, Congruence Theorems in the past, present, and future, For the Learning of Mathematics, 2023, link.
- Geometry of Roman mosaics: Antonella Perucca, Geometrie der römischen Mosaiken, link online GDM Meeting 2023 Proceedings.
- Mathematics and Society: Antonella Perucca, Minorities in mathematics, link translated for MaddMaths!, March 2022, link.
- Classifications in mathematics: Pieter Belmans (Professor), The Periodic Tables of Algebraic Geometry, Snapshots of modern mathematics from Oberwolfach, 2023-02, link.
- New Montessori material: Andy Foyen (Master Student) and Antonella Perucca, Der 50cm lange Gliedermaßstab, link, GDM Meeting 2023 Proceedings, to appear.
- Multilinguism: The effect of an educational poster on basic geometry performance and math anxiety in high-school aged second-language learners Mila Marinova (Master student), Sofie Martini (PhD student), Antonella Perucca, Christine Schiltz (Professor), and Sonja Ugen (Postdoc), preprint.
- Geometry of Roman mosaics: Marko Peric (Master Student) and Antonella Perucca, Mathematics of the Vichten Mosaic, link, preprint.
- Linear algebra and arithmetics: Antonella Perucca, Addition walls, link, preprint.
- Arithmetic billiards: Steve Mendeleev (High-school pupil), Flavio Perissinotto (PhD student) and Antonella Perucca, Three-dimensional arithmetic billiards, link, preprint.
- A formula for arithmetics and the Inclusion-Exclusion principle for multisets: Antonella Perucca, The least common multiple of several numbers in terms of greatest common divisors, link, preprint.
- Exploring mathematics with games: Thierry Meyrath (Scienteens Lab), Clara-Ioana Mincu (High-school pupil) and Antonella Perucca, Training mathematical thinking with the inclusive card game UNO, link, preprint.
- Differential geometry: Jilly Kevo (Master student), Are all Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid?, link, preprint.
- Raymond Mortini (Research guest) The generalized Eulerian power sums ∑k=1n kmzk, Mathematics Newsletter, vol. 34, 2023.
- Raymond Mortini (Research guest) Yet Another Integral Representation of Catalan’s Constant, The American Mathematical Monthly, vol. 131, 2024.
Popularization
Several members of the Department of Mathematics are involved with outreach and popularization, see in particular our outreach page.
The following popularization article is by Guenda Palmirotta (Postdoc):
The following popularization articles are by Antonella Perucca and collaborators (the articles for Uitwiskeling have been translated into Dutch and edited by Luc van de Broek):
- Article Arithmetic Billiards, Plus Magazine (University of Cambridge).
- Article Maths Around the Clock, Plus Magazine (University of Cambridge).
- Article The hardest logic puzzle ever, Plus Magazine (University of Cambridge).
- Article
Trigonometry for the multiples of 3 degrees, with Deborah Stranen (Master student), Uitwiskeling.
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Article 5-Con triangles, Uitwiskeling.
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Article The Art Gallery Problem, Uitwiskeling.
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Article The 15-puzzle, Uitwiskeling.
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Article Four points, two distances, Uitwiskeling.
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Article The seven bridges of Königsberg, Uitwiskeling.
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Article Discover multisets, Uitwiskeling.
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Article The ABCD of cyclic quadrilaterals, with Engjëll Begalla (Master student), Uitwiskeling.
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Article Every number is the beginning of a power of 2, Uitwiskeling.
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Article Staircase numbers, Uitwiskeling.
- Article Cardinalities and the continuum hypothesis, Uitwiskeling.
- Article The decimal representation of a fraction, Uitwiskeling.
The following popularization articles and videos are by Christophe Ley (Professor) and collaborators:
- Les mathématiques, un grand défi de cette pandémie, with Pierre Mangers (CEO) and Ivan Nourdin (Professor), Tageblatt, June 2020.
- Article Modélisation mathématique d’un match de football, with Léo Gerville-Réache (Professor), TANGENTE Hors-série 2023, vol. 86.
- Article De l’entraînement à la performance sportive , with Léo Gerville-Réache (Professor), TANGENTE Hors-série 2023, vol. 86.
- Maths et sports - quand les statistiques sont plus que des nombres, Maths Express, 2021, 87–92.
- Video Intelligence artificielle et science des données
- Video The usefulness of scientific models and the danger of statistical illiteracy
Miscellanea
- Our students carry on experimental projects also in the framework of the Experimental Mathematics Lab (see the gallery).
- Antonella Perucca, Beat the Prof: Ebene Geometrie, Quiz for Zeit Online.
- Antonella Perucca, Pietro Sgobba (PhD student) and Sebastiano Tronto (PhD student), Proof without words images.
- Jerry Hilgert (Master student) and Antonella Perucca, Riddelicious, mathematical riddles set in the Luxembourgish context, in
English, German, French.
- Creation of Wikipedia pages (English and German Wikipedia): Das schwierigste Rätsel der Welt, Andreas Gramsamer (Master student) and Antonella Perucca; Trigonometrische Konstante ausgedrückt in reellen Radikalen, Antonella Perucca and Deborah Stranen (Master student); 5-Con triangles Antonella Perucca; Arithmetic billiards Antonella Perucca.
- Ann Kiefer, Antonella Perucca, Christophe Tholl (Master student), Homeschooling Mathematics, survey in Luxembourgish schools for pupils and teachers about the pandemic period (authorized by the Ministry of Education), with Lime Survey, June 2021, see link.
- Mathematik zum Anfassen: Wanderausstellung des Mathematikums Gießen, Antonella Perucca and the students of the Master of Secondary Education, documentation about the exhibition of the Mathematikum-Museum, 2018, 59 pages, link.
- Antonella Perucca and Edith Wittman (Master student), Drehoskop, an instrument to investigate polyhedra, image.
- Antonella Perucca and Sebastiano Tronto (PhD student), How to become the world record holder for solving the Rubik's cube, link.
- Kim Da Cruz (Master student) and Dylan Mota (Master student) and Guenda Palmirotta (Postdoc), Escape Game Disney revisited: cartes, livret.
- Kim Da Cruz (Master student) and Dylan Mota (Master student) and Guenda Palmirotta (Postdoc), Mission : Retour sur Terre, Escape Game.
- Mélanie Thellière (Postdoc) and collaborators, 3D ruled surfaces project, link.
- Antonella Perucca,
Horizontal (An artistic reflection on the meaning of horizontal, on points of view, on different shades of right and wrong, on the meaning of words, on definitions.),
BIG (An artistic explanation of fuzzy logic.),
BIGsmall (An artistic reflection on relativity.).
- Fabio Génin (High-school pupil) and Antonella Perucca, SageMath for teachers, some pieces of advice, link.
- Antonella Perucca, Flow Rings and Guess the number MatheMAGICAL: how to be a mathemagician.