Recreational Mathematics & Didactics

Mathematical playground.

Continuum Hypothesis

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


  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Sliding mask for recurrence sequences: Antonella Perucca, Unmasking Recurrence Sequence, link, Pi in the Sky, vol. 21, 2019.
  6. 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.
  7. 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.
  8. 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.
  9. Multiplication tables: Antonella Perucca, The Easy Multiplication Tables, Poster, online material of the GDM Conference 2021, link.
  10. 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.
  11. 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.
  12. 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.
  13. Multilinguism: Antonella Perucca, Visual Mathematics Dictionary, GDM Mitteilungen, 2022, link.
  14. 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.
  15. School reality: Antonella Perucca, Multiplying mathematical teachers, GDM Mitteilungen, 2023, link.
  16. School reality: Antonella Perucca, Soft skills for mathematical teachers, GDM Mitteilungen, 2023, link.
  17. Understanding Congruence Theorems: Antonella Perucca, Congruence Theorems in the past, present, and future, For the Learning of Mathematics, 2023, link.
  18. Geometry of Roman mosaics: Antonella Perucca, Geometrie der römischen Mosaiken, link online GDM Meeting 2023 Proceedings.
  19. Mathematics and Society: Antonella Perucca, Minorities in mathematics, link translated for MaddMaths!, March 2022, link.
  20. Classifications in mathematics: Pieter Belmans (Professor), The Periodic Tables of Algebraic Geometry, Snapshots of modern mathematics from Oberwolfach, 2023-02, link.
  21. New Montessori material: Andy Foyen (Master Student) and Antonella Perucca, Der 50cm lange Gliedermaßstab, link, GDM Meeting 2023 Proceedings, to appear.
  22. 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.
  23. Geometry of Roman mosaics: Marko Peric (Master Student) and Antonella Perucca, Mathematics of the Vichten Mosaic, link, preprint.
  24. Linear algebra and arithmetics: Antonella Perucca, Addition walls, link, preprint.
  25. Arithmetic billiards: Steve Mendeleev (High-school pupil), Flavio Perissinotto (PhD student) and Antonella Perucca, Three-dimensional arithmetic billiards, link, preprint.
  26. 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.
  27. 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.
  28. Differential geometry: Jilly Kevo (Master student), Are all Weakly Convex and Decomposable Polyhedral Surfaces Infinitesimally Rigid?, link, preprint.
  29. Raymond Mortini (Research guest) The generalized Eulerian power sums ∑k=1n kmzk, Mathematics Newsletter, vol. 34, 2023.
  30. Raymond Mortini (Research guest) Yet Another Integral Representation of Catalan’s Constant, The American Mathematical Monthly, vol. 131, 2024.
  31. School reality: Antonella Perucca, Advertisement for mathematical competitions, GDM Mitteilungen, 2024, link.

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):

The following popularization articles and videos are by Christophe Ley (Professor) and collaborators:


Miscellanea