Workshops

Piet Mondrian (1872 - 1944) was a Dutch artist who loved to create beautiful paintings with colorful rectangles. When you use colored rectangles to completely cover a square canvas without leaving a single uncolored spot, you are "tessellating" the image. Tessellation is an important mathematical concept studied by many scientists. The problem becomes even more interesting when you try to use rectangles that all have different side lengths. And it gets even more fascinating when these rectangles must all have the same area.

Join us for a workshop to create mathematically beautiful pictures! No matter how old you are, with us you can try your hand at solving exciting, unsolved mathematical problems, just like the mathematicians!

Literature reference:

Natalia García-Colín, Dimitri Leemans, Mia Müßig, Érika Roldán. There is no perfect Mondrian partition for squares of side lengths less than 1001. arXiv 2311.02385, November 2023

Have you ever heard of the Fence Challenge? For this, you need 12 pentominoes, each linked to a zodiac sign.

Your task: Use some or all of the 12 zodiac signs to build a fence on the square grid. The goal is to construct the fence in such a way that it encloses as large an area as possible. Make sure that your fence is well-closed. Good luck!

The best thing about it: you can tackle the challenge alone or in a team.

The Fence Challenge is a Citizen Science project. Your solution can help us make progress in solving this currently open mathematical problem. Are you ready to dive in and give it a try? Show us what you've got!

For more information, all the materials you need for this challenge, and a mixed reality experience, please visit: FENCE CHALLENGE.

Literature references:

Fr V Feser. Pentomino farms. Journal of Recreational Mathematics, 1, Seiten 675–682, 1968
Martin Gardner. Mathematical games. Scientific American, 228, No. 2, Seiten 106—109, Februar 1973
Alexis Langlois-Rémillard, Mia Müßig und Érika Roldán. Extremal fence problems with polyominoes, 2024+. In Vorbereitung.
Takakazu Shimauchi. Pentomino farm. Sugaku Seminar, Seiten 11–16, März 1978

In this workshop, we will work together on puzzles using so-called MacMahon cubes. These cubes have each face colored with one of six colors. Many puzzles can be played with these cubes and we focus on one called “Eight Blocks to Madness”. The puzzle is to select a target cube, and then pick eight additional cubes to arrange in a larger 2x2x2 cube with the same coloring as the target. We will play with this puzzle, learn about solution strategies, and find other interesting results related to these cubes.

Literature reference:

Inga Johnson, Érika Roldán. Solution Numbers for Eight Blocks to Madness Puzzle. arXiv 2407.13208, Juli 2024

Graph coloring and its variants are amongst the most important combinatorial optimization problems, both for their theoretical importance but also for its applications in real scheduling problems.

However, coloring a graph and variants of this problem are hard mathematical and computational mathematical problems, despite their apparent simplicity.

In this workshop, we will interact with graphs to solve different coloring problems and we will see also how an artificial intelligence running in a computer performs on this task, and what can we improve.

Workshop & Happening accompanied by a talk. Place with us regular polygons that do not tesselate the Euclidian plane to simulate a cell growth process.

This process is based on the so-called Eden Model which is quite simple. We will start with a single polygon with the goal is to create a random geometric structure that will grow as new polygons are attached. The only two rules are that the new polygon has to share a side with any other polygon already in place and that there cannot be overlaps. In tis workshop, we will compare topological and geometric properties with computer-simulated samples such as the one depicted above.

This event is based on the following joint research paper:

Claudia Silva, Érika Roldán, Rosemberg Toala-Enriquez. Eden model for Pentagons. arXiv:2403.12772,  March 2024 - accepted for publication at Bridges proceedings - top-notch conference in math + art + design + architecture

This workshop is co-produced with the independent cultural platform DESFOGA. .