Recreational Mathematics & Didactics

Mathematical playground


Algebra

  • CHINESE REMAINDER THEOREM: The Chinese Remainder Clock, College Journal of Mathematics, vol. 48, no. 2, March 2017, 82-89, link.
  • ARITHMETIC BILLIARDS: with 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; with Steve Mendeleev (high-school pupil) and Flavio Perissinotto (PhD student), Three-dimensional arithmetic billiards, link, preprint.
  • GCD & LCM: The least common multiple of several numbers in terms of greatest common divisors (and the Inclusion-Exclusion principle for multisets), link, preprint.
  • MULTISETS: Multimengen für die Arithmetik, Beiträge zum Mathematikunterricht 2019, WTM-Verlag Münster, 613–616, link, see also Multisets in arithmetics, link.
  • RECURRENCE SEQUENCES: Unmasking Recurrence Sequence, link, Pi in the Sky, vol. 21, 2019; with the MSE-M Master Students 2024, Funnier arithmetic sequences, link.
  • MASTERMIND: with Tom Fiore and Alexandre Lang (undergraduate student), 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.
  • ESCAPE GAMES: Mathematical Escape Game, Sample Riddle, link.
  • MULTIPLICATION TABLES: The Easy Multiplication Tables, Poster, online material of the GDM Conference 2021, link.
  • PROPORTIONS: with Pit Ronk (Master student), Beware Proportions, link (we had also planned a proportionality calculator, now superseded by AI).
  • MENTAL CALCULATIONS: with Rich Andrusiak, Parallel Computing and the Value of Teamwork, Mathematics Teacher: Learning and Teaching Pre-K-12, vol. 115, no. 1, 2022, 62-65.
  • LINEAR ALGEBRA FOR ARITHMETICS: Addition walls, link, preprint.
  • ARITHMETICAL MAGIC: MatheMAGICAL Guess the number (how to be a mathemagician).

Geometry

  • POLYGONS: with Emiliano Torti, Congruence Theorems for convex polygons involving sides, angles, and diagonals, International Journal of Geometry, vol. 12, no. 1, 2023, 83-92, link.
  • TRIANGLES AND QUADRILATERALS: with Nathaniel Sagman and Guillaume S. Verfaillie (Bachelor student), Congruence Theorems involving heights for triangles and convex quadrilaterals, International Journal of Geometry, vol. 14, no. 2, 2025, 76-85.
  • RUBIK SNAKES: with Francesco Grotto and Tatjana Van Steenbergen Bergeron (high-school pupil), Rubik Snakes on a plane, College Mathematical Journal, vol. 55 no. 4 2024, 317-327.
  • PYTHAGOREAN TRIPLES: with 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.
  • ROMAN MOSAICS: with Marko Peric (Master Student), Mathematics in the Vichten Roman Mosaic, link, J. Humanist. Math. vol. 15, no.1, January 2025, 306-316 (and Geometrie der römischen Mosaiken, link online GDM Meeting 2023 Proceedings).
  • TRIANGLES: Understanding Congruence Theorems: Antonella Perucca, Congruence Theorems in the past, present, and future, For the Learning of Mathematics, vol. 43 no. 2 2023, 17-19. link.
  • FOLIATIONS: Foliazioni semiolomorfe e sottovarietà Levi piatte di una varietà complessa, my Master thesis pdf and its summary pdf.
  • EXHIBIT: with Edith Wittman (undergraduate student), Drehoskop, an instrument to investigate polyhedra, image.
  • GEOMETRIC MAGIC: Flow Rings
  • QUIZ: Beat the Prof: Ebene Geometrie, Zeit Online.
  • RIBBONS (one algebraic-geometric exercise): Birthday presents Math, pdf.

Miscellanea

  • MATHEMATICS OF CHOICES: with Alexandre Benoist (PhD), Johanna Hoffmann (pupil) and Lucile Turquin (pupil), Choosing the movie for a movie night, link.
  • INDUCTION (domino effects): with Milko Todorovic (Master student), Visualizations for the Principle of Mathematical Induction, link, Veranschaulichungen des Induktionsprinzips, Beiträge zum Mathematikunterricht 2019, WTM-Verlag Münster 2020, 705–708. See also: slides.
  • PROBABILITY (one riddle): The improbable outcome, pdf.
  • ANALYSIS: Intermediate value theorems for the rationals, pdf.
  • NUMERAL SYSTEM: with Paul Deutsch (pupil) and Dany Leal Cordeiro (Master student), The Wallet Problem, link.
  • WIKIPEDIA: (creation of pages in English and German) 5-Con triangles; Arithmetic billiards; Das schwierigste Rätsel der Welt, with Andreas Gramsamer (undergraduate student); Trigonometrische Konstante ausgedrückt in reellen Radikalen, with Deborah Stranen (Master student).
  • IMAGES: with Pietro Sgobba and Sebastiano Tronto (PhD students), Proof without words images.
  • RIDDLES: with Jerry Hilgert (Master student), Riddelicious, in English, German, French.
  • MATHEMATIKUM: with the MSE-M students 2018, Mathematik zum Anfassen: Wanderausstellung des Mathematikums Gießen, link.
  • MATH SOFTWARES: with Fabio Génin (high-school pupil), SageMath for teachers, link.
  • INCLUSION: Minorities in mathematics, link translated for MaddMaths!, March 2022, link.
  • ARTISTIC: Ceci n'est pas un carré (An optical illusion) 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.).
  • MATH MUG: Mug for number theorists.
  • INCLUSIVE MATH: Image A female mathematician, in a magic setting (2024) Open AI ChatGPT.

For didacticians

  • with Andy Foyen (Master student), Der 50cm lange Gliedermaßstab, link, GDM Meeting 2022 Proceedings, Beiträge zum Mathematikunterricht 2022, WTM-Verlag Münster 2023, 741-744.
  • with Olha Nesterenko, Numeral coins as hands-on material, material for digital tools, and for the conceptual understanding of numeral systems, link, GDM Meeting 2024 Proceedings.
  • with Thierry Meyrath and Clara-Ioana Mincu (high-school pupil), Training mathematical thinking with the inclusive card game UNO, link, preprint.
  • Visual Mathematics Dictionary, GDM Mitteilungen, 2022, link.
  • Multiplying mathematical teachers, GDM Mitteilungen, 2023, link.
  • Soft skills for mathematical teachers, GDM Mitteilungen, 2023, link.
  • Advertisement for mathematical competitions, GDM Mitteilungen, 2024, link.
  • Didactics without borders, GDM Mitteilungen, 2024, link.
  • Friendly mathematical exercises, GDM Mitteilungen, 2025 link.
  • Math CEO (of AI), GDM Mitteilungen, 2025 link.
  • A didactical reflection on varying quantities, to appear in GDM Mitteilungen, link.
  • Mathematical competencies, link.
  • Choosing female role models in mathematics, link.
  • with Ann Kiefer and Christophe Tholl (Master student), Homeschooling Mathematics, survey 2021, link.
  • with Mila Marinova, Sofie Martini, Christine Schiltz and Sonja Ugen, The effect of an educational poster on basic geometry performance and math anxiety in high-school aged second-language learners, preprint.

Popularization articles

The following articles for Plus Magazine (University of Cambridge) have been edited by Marianne Freiberger:

  • Arithmetic Billiards, pdf
  • Maths Around the Clock, pdf
  • The hardest logic puzzle ever, pdf

The following articles for Uitwiskeling have been translated into Dutch and edited by Luc van de Broek:

  • with Deborah Stranen (Master student), Trigonometry for the multiples of 3 degrees, pdf
  • 5-Con triangles, pdf
  • The Art Gallery Problem, pdf
  • The 15-puzzle, pdf
  • Four points, two distances, pdf
  • The seven bridges of Königsberg, pdf
  • Discover multisets, pdf
  • with Engjëll Begalla (Master student), The ABCD of cyclic quadrilaterals, pdf
  • Every number is the beginning of a power of 2, pdf
  • Staircase numbers, pdf
  • Cardinalities and the continuum hypothesis, pdf
  • The decimal representation of a fraction, pdf