Who doesn't know it - there's a delicious cake topped with various fruits and chocolate and people argue about how it could be divided fairly. If everyone has different preferences, this can get quite complicated, especially if there are more than 2 people.

In this workshop we want to deal with different types of fair sharing. After a short introduction, you get to work yourself: What options are there to share the cake so that everyone is satisfied? And is that really practical or does it just look good on paper? How can thieves divide a pearl necklace with different types of pearls between them without having to do much cutting? And how can a (topological) statement about a house with many doors help us share a cake fairly?

In this workshop you are asked to think together, try things out and prove it.

_{Recommended for 7th year and above}

We come across graphics again and again in everyday life - even if we may not even notice it. They are clearly visible in local public transport network maps, for example, but can also be used in the background to plan tram and bus connections.

We briefly introduce the field of graph theory and the principle of induction. You will then have the opportunity to use graphs to get to the bottom of exciting questions at four different stations: How many cameras do you need to monitor a museum? How many colors does it take to color any map? And does this really apply to every card? Which graphs can be drawn so that the lines do not cross each other? And when can that be done without putting down the pen?

In this workshop you have a lot of time to think, discover and prove yourself.

_{Recommended from 8th grade and above}

Mathematics is a hidden side of many games, without us realising it's there at all. In this workshop we want to talk about a unique game: Dobble. Dobble is a card game, with lots of different symbols on every card. What is special about those cards is that any two cards have exactly one symbol in common. The goal is to find that symbol as quickly as possible. Sometimes that's really easy but at other times it can be an almost impossible task. But, how difficult is it to build such a game yourself? And could we build Dobble games with a random number of cards or symbols? In order to find the answers to these questions we'll travel into the world of projective geometry, which has a lot in common with the Dobble game. The characteristics of projective geometry will help us to understand the game from a mathematical point of view.

In this workshop you will have the opportunity to play the game yourselves and then, after learning a bit about projective geometry, build your own game and use our stations to discover even more.

_{Recommended for 9th year and above}

Topology is a branch of mathematics that isn't all that different from geometry. It's about the shape and properties of objects in a topological space. One peculiarity of topology we'll talk about: We consider two objects to be the "same" if you can turn one into the other by twisting, stretching and crumpling it – as long as you don't cut or tear it. That means that a sphere and a cube are the same object. Therefore we need different criteria in order to tell objects apart. One of those is the Euler characteristic, which analyses whether curves on objects can be contracted. 

This workshop takes you from Euler's polyhydron formula over graphs and holes to the general Euler's characteristic. A central point here is to "grasp" the objects – literally. With the help of many models and examples you can discover the particularities of topology yourselves and find out what it's all about. We will formulate and prove Euler's polyhydron characteristic together and understand the relations between the different objects.

After the mathematical introduction you can experience the theory hands on at stations with every day objects and games: Why does a football always look the way it looks? What would happen if you did tear and make a hole? And how can Euler help to win every game of Brussels Sprout?

_{Recommended for 8th year and above}

If we want to tile our bathroom or kitchen, there should be no holes between the tiles, and the tiles shouldn't overlap either. In mathematics we also call this lining of a plane with tiles tiling. There are many different tilings, we can use different tiles or only the same type of tile. Sometimes the pattern repeats after a while and sometimes it doesn't.

This workshop consists of different modules. In a general section we want to examine the basic properties of tilings and describe and classify them mathematically.

Afterwards we can, depending on your interests, time and level discover different aspects of plane tilings:

• Tilings by polygons: In this module we'll examine polygonal tiles. You can find out with which polygons the plane can be tiled. Then we'll look at archimedean tilings and we'll find out together how many of those can exist.
• Penrose tiling: A penrose tiling consists of only two types of tiles. If you follow certain matching rules the pattern will inevitably be aperiodic. We want to take a closer look at the penrose tiling together and find out why it's always aperiodic.
• Aperiodic tilings: Aperiodic tilings never repeat themselves, no matter how big they are. Up until now every kind of aperiodic tiling needed more than one type of tile. Only in spring 2023 the "Einstein" tile was discovered, that's the only tile that (with it's mirror image) tiles the plane aperiodically. In this module you'll learn, what the tile looks like, why it tiles aperiodically and how with this single solution silmultaneously an infinite number of Einstein tiles where found.
• Spheriacal and hyperbolical tilings: If we only consider regular polygons, there are only a limited number of variations, how the plane can be tiled with them. But if we move to the sphere or the hyperbolic plane we discover undreamed-of possibilities. We also introduce those other geometries and their properties. 

_{Recommended for 7th year and above} 

In our every day life we encounter symmetrival patterns all the time, without paying attention to them. We find them on pavements, grandma's floral wallpaper and on the wall of the almost 1000 years old fortress Alhambra. But what does that even mean - symmetrical? And what do these patterns have to do with mathematics? 

In our workshop we'll get to the bottom of these questions and learn about the mathematics behind so called wallpaper patterns. We will find out how we can mathematically tell two patterns apart and determine with these criteria how many different types of wallpapers exist.That way we can not only design our own wallpaper patterns, but also identify which type of wallpaper we can find in grandma's living room.

If you discover a pattern and want to know what mathematics could be behind it, bring it along! It could be a t-shirt or a scarf, a patterned bowl or a photo of grandma's wallpaper.

_{Recommended for 8th year and above}

The Rubik's Cube was invented in 1974 by Ernö Rubik, a Hungarian civil engineer and architect, so his students could train their spatial sense. By now the colourful, revolvable cube fascinates people all around world - or nearly reduces them to despair. 

We want to get to the bottom of the Rubik's Cube's magic together, by studying the cube from a mathematical point of view. In order to do that we'll enter the world of group theory. First we'll introduce the basic concept of mathematical groups and then find out what they have to do with the Rubik's cube. Then we'll have to figure out how to mathematically describe the cube. All of that will help us with the consideration of the (theoretical) solubility of the Rubik's cube, when we'll show together how to tell, from looking at a scrambled cube, whether it can be solved.

Besides the theory there will be many stations where you can discover further groups and experiment with the Rubik's cube yourselves.

_{Recommended for 11th year and above}

We regularly offer Workshops in line with the Girl's Days. Our workshops ar usually aimed at students from the years 5 to 10, but they are interesting for older students as well. You can register through the Girls Day Radar.

The workshops take place within the context of the MINTmachen! projects, they are preceded by an intresting lecture from the field of research.