Permanent exhibition included in the day ticket
The Fascination of Mathematics – where magic, geometry and logic come together.
Mathematics is often seen as abstract. At phaeno, however, it comes to life. It’s not about memorising formulas, but about discovering things for yourself, trying things out and marvelling at the results. When you experiment, you suddenly recognise patterns, connections and laws that would otherwise remain hidden.
This leads to genuine ‘aha’ moments that show: maths is creative, surprising and full of fascinating ideas.
Mathematics is all around us. It is found in the architecture of phaeno, in works of art and in nature. In everyday life, we come across it when baking cakes, pitching tents, painting the house and even when laying the table. We all use mathematics more than we realise!
At the same time, maths enables impressive innovations. It helps us to design spectacular structures, optimise traffic flows and develop new materials for research and medicine.
In the ‘Mathemagie’ exhibition area, visitors discover the fascinating world of maths in a playful way. Whether it’s astonishing shapes, optical illusions or tricky brainteasers: here, interactive exhibits make abstract concepts playfully visible and understandable. And best of all: the results are not only surprising, but often beautiful too. This turns mathematics into an experience for families, children, young people, school groups and adults.
Step onto the surface and find out. In the exhibition Boundaries, invisible territories emerge around you and the other visitors, which suddenly become visible through boundary lines.
Behind this lies the mathematical principle of the Voronoi diagram: everyone is allocated the space closest to them. But be careful: even a small step shifts the boundaries. What looks like a game helps researchers to plan cities, optimise mobile networks or understand natural structures such as honeycombs and crystals. Discover how mathematics brings order to chaos and constantly redistributes space.
The ‘Maths Magic’ section is particularly suitable for school classes of all types. Topics such as geometry, symmetry, motion, pattern formation and mathematical modelling are taught here in a clear and practical way. The exhibits complement maths lessons by encouraging hands-on experimentation and foster problem-solving skills, spatial awareness and, above all, curiosity about STEM subjects.
Where do you think each individual grain of sand falls? Give it a go and transform a simple sandpit into a landscape full of mountains, valleys and mysterious lines. As the sand trickles through the holes, fascinating patterns emerge as if by magic – known as Voronoi diagrams.
Take a close look: where do the different areas meet? And why do the boundaries run exactly there? The secret behind this has to do with a clever idea from mathematics. Using the same patterns, you can even work out which town, shop or hospital is closest. Here you can discover how amazing order emerges from lots of tiny grains of sand.
We’re also hoping for plenty of maths magic for our younger guests and the teaching staff. One particularly enchanting aspect is the symmetry of snowflakes.
How on earth is the straight red rod supposed to fit through the recess in this curved shape?
Trying it out reveals the secret: the recess forms a hyperbola, a special mathematical curve. If you thread the rod through and rotate it, a hyperboloid surface is created – an elegant geometric shape that looks curved but is in fact made up entirely of straight lines.
Such structures fascinate more than just mathematicians; they also play an important role in architecture and engineering.
Amazement guaranteed: the red rod glides effortlessly through the cut-out and traces a seemingly impossible shape in the air. A stunning example of how our eyes can sometimes deceive us – and that geometry is full of surprising magic!
Experience the transition from flat 2D shapes to vivid 3D bodies! At this station, you can rotate two-dimensional cards with imprinted motifs. The rotation creates exciting three-dimensional bodies from the flat shapes - a fascinating experiment in geometry!
There are four different shapes that you can try out:
What exactly is happening here? You will experience solids of revolution that are created when a 2D surface is rotated around an axis. You will be familiarised with the mathematical concepts of rotation, volume calculation and symmetry. You will see live how angles and axes affect the shape.
The experiment brings maths and art together and shows how abstract mathematical ideas become visible and tangible. It is an exciting experience for anyone who enjoys science and maths!
In this exciting experiment, you can organise a race with balls on two tracks – one of which is longer than the other. Surprisingly, the track with the longer distance wins!
Why is that? The longer track is what’s known as a brachistochrone – the quickest way to get from one point to another. It’s not just about the length of the route, but also about its path and gradient. Both balls start at the same speed, but reach the finish at different times – the ball taking the ‘detour’ is faster!
In our maths area, there are stations with one, two or three tracks that illustrate different aspects of the brachistochrone and show you how speed and motion are linked in surprising ways.
A fascinating example of optimisation and mathematics in physics, which clearly explains the laws of motion!
Artistic exhibits such as Arthur Ganson’s *Machine and Concrete* complement the exhibition’s scope and demonstrate just how much our everyday lives – and indeed art itself – are influenced and even inspired by mathematics. These installations straddle the boundary between art and science, provoking questions that lead to entirely new questions and discoveries.
Take Arthur Ganson’s ‘Machine and Concrete’, in which 25 wheels are interlocked. The first wheel turns quickly. And the last one would only start turning after trillions of years. That is why the artist simply cast it in concrete. An invitation to reflect on the passage of time and our perception of it. It shows that mathematics is not just about calculations, but can also inspire wonder, philosophical reflection and the discovery of new perspectives.
