Didactics
MATHEMATICS IS COLORFUL !!
The Chinese Remainder Clock
A mathematical clock based on the Chinese Remainder Theorem.
Math around the Clock
Various original mathematical clocks.
Visualizing recurrence sequences
A sliding mask to visualize the recurrence relation for the Fibonacci sequence and any other recurrence sequence.
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 Mastermind Wheel
A didactical tool for understanding Knuth's algorithm for winning Mastermind in at most five moves.
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).
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.
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).
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)