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.

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.

Visualizing recurrence sequences

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

• Unmasking recurrence sequences, pdf, to appear in Pi in the Sky (Issue 21, 2018).

This original idea was appreciated by the mathematikum because they changed accordingly the exhibit about the Fibonacci numbers.

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.

• Creation of the Wikipedia page 5-Con triangles.
• 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.

• Creation of the Wikipedia page Arithmetic billiards.
• The article Arithmetic billiards in Plus Magazine.

PytEuk Puzzle

A mathematical exhibit around Pythagoras' Theorem.

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

Multisets in Arithmetic

About the multiset of prime factors.

• Multisets in Arithmetic, article (submitted): divisibility properties are analyzed through the multiset of prime factors (in particular, the lcm for several numbers is expressed in terms of the gcd).
• Discover multisets, pdf, self-study material for talented pupils.

The 135 Exhibit

Placing the numbers 1,3, and 5.

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

Classroom Posters

A mathematical posters to learn notions around angles.
Created in collaboration with Alison Adams and Alexandre Lagarmitte. Free for personal use or for use in the classroom (non-commercial use only).

• Angles (the poster in English).
• Angles (the poster in French).

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, creation of the Wikipedia page Trigonometrische Konstante ausgedrückt in reellen Radikalen.
• with Deborah Stranen, the article Trigonometry for the multiples of 3 degrees, to appear in Uitwiskeling translated by Luc Van den Broeck.

Mathematical riddles

The most difficult logical riddle.

• with Andreas Gramsamer, creation of the Wikipedia page Das Schwierigste Rätsel der Welt.

Mathematical riddles for everyone.

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

Mathematical Induction

Illustrating the Principle of Mathematical Induction.

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

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).

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, from The Hunger Games.

The Art Gallery Problem.

• An introductory article about the Art Gallery Problem.