Didactics

The Chinese Remainder Clock

A mathematical clock based on the Chinese Remainder Theorem.

• The official webpage of the CR-Clock: there you find articles, animations, and you can download a free App with the clock!

Math around the Clock

Various original mathematical clocks.

• The article Maths Around the Clock in Plus Magazine.
• Various original mathematical clocks.

Visualizing recurrence sequences

A sliding mask to visualize the recurrence relation for the Fibonacci sequence and any other recurrence sequence.

• Unmasking recurrence sequences, Pi in the Sky (Issue 21, 2019).

Multisets in Arithmetic

About the multiset of prime factors.

• Multiset in Arithmetic, article: divisibility properties are analyzed through the multiset of prime factors (in particular, the lcm for several numbers is expressed in terms of the gcd). A german version of this article, Multimengen für die Arithmetik, will appear in the Proceedings of the GDM Tagung in Regensburg 2019.
• Discover multisets, pdf, self-study material for talented pupils, adapted for Uitwiskeling by Luc Van den Broeck (to appear).

Mathematical Induction

Illustrating the Principle of Mathematical Induction.

• with Milko Todorovic, the article Visualizations for the Principle of Mathematical Induction (here the Slides) about the variants of the Principle of Mathematical Induction and how to illustrate them.

Mathematical Quizzes

One Quiz about plane geometry.

• The Quiz (in German) Beat the Prof: Ebene Geometrie, published on Zeit Online on December 2, 2018. The Quiz is without time limit, and it is highly recommended to all future math teachers.

The Mastermind Wheel

A didactical tool for understanding Knuth's algorithm for winning Mastermind in at most five moves.

• The Master Mind Wheel and some introductory Slides.
• with Thomas M. Fiore and Alexander Lang, Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind, The College Mathematics Journal, Volume 49 (2018) Issue 4, 278--286.

Sim!Cong!

A didactical card game for learning the Congruence and Similarity Theorems for triangles.

• Sim!Cong!, The instructions and the set of printable cards (free for personal use, or use in class for instructors).
• Leaflet, Guidelines for commercial use (University of Luxembourg).

5-Con triangles

Triangles that are almost congruent.

• The article Driehoeken met onderling 5 gelijke zijden en hoeken, translated and edited by Luc Van den Broeck, Uitwiskeling, Jaargang 34, Nummer 3 (Zomer 2018).

Arithmetic billiards

A geometric construction for the gcd and the lcm.

• The article Arithmetic billiards in Plus Magazine. An addition which is joint work with Bruno Carvalho da Veiga pdf.

Classroom Posters

Mathematical posters to learn the multiplication tables.
Created in collaboration with plan K. Free for personal use or for use in the classroom (non-commercial use only).

• Multiplication tables.
• Multiplication tables and factorizations (for math-enthusiasts).

Mathematik zum Anfassen

Documentation about the mobile exhibition of the mathematikum.

• With the students of the Master of Secondary Education, the detailed description of the exhibition Mathematik zum Anfassen of the mathematikum.
• With Bruno Teheux, slides explaining some of the exhibits.

History of mathematics.

The Babylonian tablet Plimpton 322.

• with Deborah Stranen, the article Understanding the Babylonian tablet 'Plimpton 322' with the decimal system (here the Slides).

"Understanding the Babylonian table 'Plimpton 322' with the decimal system" makes an interesting contribution to the history of mathematics. (Reviewer)

Trigonometry

Sines and cosines expressed by radicals.

• with Deborah Stranen, the article Veelvouden van 3 graden, translated by Luc Van den Broeck, Uitwiskeling, Jaargang 35, Nummer 2 (Lente 2019).

Mathematical riddles

The Hardest Logic Puzzle Ever.

• The article The Hardest Logic Puzzle Ever, to appear in Pi in the Sky.

Mathematical riddles for everyone.

• with Jerry Hilgert, Riddelicious, mathematical riddles set in the Luxembourgish context, in English, German, French.

Further mathematical exhibits

Drehoskop (to explore solids).

• With Edith Wittman, Drehoskop, a tool to detect rotational symmetries for polyhedra (these can rotate on various axes).

A mathematical exhibit around Pythagoras' Theorem.

• PytEuk, an exhibit that shows Pythagoras' Theorem and some related result by means of puzzles.

Placing the numbers 1,3, and 5.

• The 135 Exhibit, with two formulas related to the number 135, pdf.

GoFlex (composable flexible stripes).

• GoFlex, reconfigurable flexible stripes to create Möbius bands and other geometrical objects.

Further mathematical projects

Mockingjay Mathematics (movie-inspired problems).

• A movie-inspired mathematical exercise sheet, Mockingjay Mathematics.

The Art Gallery Problem.

• The article Het kunstgalerijprobleem, translated by Luc Van den Broeck, Uitwiskeling, Jaargang 35, Nummer 3 (Zomer 2019).

The 15-puzzle.

• An introductory article about the 15-puzzle, submitted.

The 'Four points, two distances' problem.

• An article with the problem's solution, submitted.

Creation of Wikipedia pages

(Permission to use the Wikipedia logo can be found here)

• 5-Con triangles.
• Arithmetic billiards.
• with Andreas Gramsamer, Das Schwierigste Rätsel der Welt.
• with Deborah Stranen, Trigonometrische Konstante ausgedrückt in reellen Radikalen.