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Mathmagic



This area of the exhibition is dedicated to probably the greatest natural phenomenon anywhere: human perception. Here, you can experience yourself as a phenomenon.

Amazing experiments show how sensory stimuli and perception are connected and which individual mindscape the brain constructs in this process. Many exhibits will surprise you even as you walk by them: you won't discover what your brain is automatically trying to correct until you are just a few steps away from the Reversed Perspective exhibit, for example.

And because dialogue is often the only way to verify much of what we believe to be our perception, the exhibition as a whole is presented in a highly interactive way. So, prepare to be especially fascinated by the Machine to be another with which you can find out how it probably feels to be in another person's shoes.

The Rotating Tunnel that pinpoints the role of sight in keeping your balance is a particularly great exhibit for visitors with a strong stomach! The Ames Room and the Distorted Room will also amaze and fascinate visitors with optical illusions
Exhibit-Links
10228 Haupt

A riddle for intelligent and patient people

Puzzles for the sharp-minded and patient. Trickier than it seems: these eleven puzzles with strings, boards, and rings are challenging. One of them cannot be…

10442 Haupt

A Table with loose Legs

Three, two, one – stable. How many supports do we need to stabilize a tabletop? Without screws, without glue, of course. Sharp-minded (and experimental)…

10012 Haupt

All Triangels are the same

Central projection: Using various triangular shapes to cast congruent shadows onto a patterned wall with equilateral triangles.

10398 Detail

Angled Mirrors

Many polygons. Two mirrors positioned around an axis at various angles: a simple way to create shapes with many sides (polygons). At certain angles,…

10240 Haupt

Ball in a Bowl

Shorter path = faster to the goal? A question that occupied the best mathematicians three hundred years ago. This competition compares two parallel tracks,…

10034 Haupt

Beam Bridge

The simplest form, but not the most stable. This bridge demonstrates the forces acting on a straight beam when it is loaded and supported only at its two…

10226 Haupt

Break the code

Qxpoa gvp pbuu: Cryptography. An encrypted text appears on the monitor. The challenge is to decrypt it with as few errors as possible. But there are over four…

10032 Haupt

Bridge the Gap

Building bridges is not so easy - especially when you are not allowed to use nails, screws or glue! Here you only have nine identical wooden blocks at your…

10225 Phänomen

Catenary Arch

Building solid – like the Romans. An arch as a delicate structure: reconstructing what the Romans perfected. Understanding what gives their elegant arches…

10525 Haupt

Chance Happenings

Capturing randomness – with dice. Four faces of these dice are white. The other two faces show a red circle. After each roll, the dice with the red circle…

10980 Haupt

Changeable Weather

How do you determine the average value of numerous individual measurements? Here, the average monthly rainfall can be determined experimentally.

10058 Haupt

Christmas Balls

Round shapes, angular gaps. The spheres are indeed round, despite the triangular gaps between them. Can this really be? If a sphere is missing in the…

10224 Detail

Conic Sections with Laser

Ellipse, parabola, hyperbolic branch, or hyperbolic arm: Cross-sections of a plane through a geometric body. In this case, a cone. A laser beam circling the…

10059 Haupt

Conway Cube

Test your spatial imagination. Assemble nine pieces to form a cube. Three 1x1x1 cubes and six 2x2x1 cuboids. It seems simple, what the renowned British…

10526 Detail

Diced Snake

At some point, it’s probably going to work... All sixty dice lined up: what number shows the head of the snake? Now move forward by that number. Roll the…

10100 Haupt

Disappearing Ghost

The ghost disappears. Where did it go? The ghost reappears. Where did it come from? A puzzle made of three parts: one base element, two pieces to swap. How…

10487 Haupt

Do they fit in the Box?

Too big. Or is it? The cube fits into the glass cube. Clear enough. But the pyramid, the star-shaped object? Too big. Some objects appear larger than they…

10530 Haupt

Drawing on the Move

Elegant circles, spirals, and ellipses. Above a disc with variable rotational speed lies a ruler. If the pen is held still along the ruler, circles are drawn.…

10098 Haupt

Efron’s Dice

Loaded dice. The numbers on the faces of these four dice are nothing like what we’re used to. And they really get your brain working. The first player picks…

10399 Haupt

Elliptical Mirror

This έλλειψις has only one goal. At one focus of this mirrored ellipse stands a rotating periscope. At the other focus, a colored cone. Looking at the…

10440 Haupt

Encoding Text - Caesar’s disc

« Caesar’s Wheel » Encoding and decoding with two rows of letters that can be shifted relative to each other. Even in Caesar’s time, information was protected…

10160 Haupt

Equal Times

Meeting – in the middle. On this track, a tautochrone, the time it takes for a ball to reach the lowest point is always the same. If we release two balls,…

10116 Detail

Escher’s endless Staircase

Ascending downwards. Luckily, this infinite staircase doesn’t exist in our world. It leads upwards endlessly, without ever reaching a top. Similarly, its path…

10503 Detail

Find the Fish!

Fits, from head to fins. The fish, the wire frame next to the image, fits in only one spot into the pattern with the "water lilies." The pattern with many…

10403 Haupt

Gothic Arch and Flying Buttress

With pillars and arches. Like in a cathedral: this is how forces act in a structure with a tall pointed arch and a system of buttresses. What significant…

10507 Detail

How big is a Million?

Incredibly large. 999,999 yellow balls in a glass cylinder – and one black one. Where is it? What is a million? Through the search, a concrete task turns an…

10499 Haupt

How many Smarties?

Estimate – and verify. The many colorful Smarties are tempting – and they spark curiosity. How many are there? Many, very many, maybe thousands. How many…

10208 Detail

Hyperbolic Slot

Straight rod passes through a curved slot. Impossible, that’s the first thought. But the experiment proves otherwise. The straight rod moves without contact…

10209 Haupt

I am a function

Three steps forward, one step back. The point on the screen moves along. The curve displayed on the screen is the target. Goal: move closer, move away, and…

10441 Haupt

Ink Fractals

Fingers grow fingers. As the ink spreads between the two acrylic plates, beautiful fractal patterns form. Finger-like structures that resemble ink…

10247 Haupt

Leonardo’s Bridge

Clever: How Leonardo da Vinci builds a lightweight bridge. No screws, no nails, no ropes; just a few planks. From these, he creates a sturdy bridge. An idea…

10256 Haupt

Lights ON

Seven lights, seven buttons. The goal: make all seven lights turn on – or none at all. Pressing a button affects three lights and causes a state change: from…

10053 Haupt

Loose Stone Bridge

Brilliantly strong and simple. Loose stones, assembled in the correct order, form a bridge capable of bearing weight. Even in a small format, it can support…

10278 Haupt

Machine with Concrete / Machine set in Stone

The Eternity Machine. Twelve worm gear mechanisms for eternity! An impressive example of mathematics illustrated mechanically. With each successive gear, the…

10529 Haupt

Misty Messages

Two patterns, one image. From a distance, the surface on the plate looks like grey fog. But when we place a second plate exactly on top, an image is…

10288 Haupt

Möbius Cube Loop

Infinite puzzle. The Möbius strip, assembled from cubes. The building blocks are cubes and corner pieces. The faces of the cubes are painted on their…

10289 Haupt

Moebius Strip

Loop without end. Most things have two sides, but not everything. Among the exceptions is the Möbius strip. When we ride along it with a small train, we…

10290 Haupt

Moiré

It’s all a matter of perspective. Black point clouds: this impression is created by two perforated plates mounted one behind the other at a certain distance.…

10296 Haupt

Mozart’s Dice Music

Compose like Mozart. Roll the dice 16 times, select 16 bars, and voilà – a composition: as simple as that, according to Mozart. Following his idea, composing…

10455 Haupt

Non-round Wheels

And yet they roll! With the right rolling surface, even a square rolls perfectly round. This applies to a pentagon as well as to any other regular…

10315 Haupt

Penrose Parquet

Aperiodic pattern. In the aperiodic Penrose tiling, subpatterns repeat irregularly, even though shapes like hexagons or stars appear throughout. Using only…

10331 Haupt

Pi

The first 20,000 decimal places. π, the mysterious number – displayed as a digit spiral on a poster. π (Pi) is a natural constant that represents the ratio…

10040 Haupt

Population Growth

How fast – and where? Current population figures displayed on a world map, by continent and overall. For each continent, the counters show how many people…

10364 Haupt

Pythagoras’ Theorem - Easy to weigh up!

a² + b² = c² with stars and bunnies. The square of the hypotenuse and the squares of the legs can be weighed against each other, as they are made of identical…

10363 Haupt

Pythagoras’ Theorem - flows from this

a² + b² = c² The Pythagorean theorem describes a transformation of areas. In a right triangle, the sum of the squares of the two shorter sides equals the…

10346 Haupt

Quasi-Crystals

Golden rhombohedra. When correctly assembled, the various bodies (cubes stretched along their diagonals and cubes compressed along their diagonals) form a…

10355 Haupt

Rhombo Puzzle

Rhombo-dodecahedron from parallelepipeds. Twelve building blocks (each consisting of two connected parallelepipeds) can be assembled to form a…

10430 Haupt

Rocking Roller - the Oloid

Wobbles, but goes straight. The oloid has only one surface. It is the only known shape that fully unwinds as it rolls. This means that every point on its…

11575 Detail II

Sculptures in stroboscopic light

« BLOOM Revelation » and « BLOOM Accordance ». Sculptures come alive: single images, shown in rapid succession, are combined by our brain into a seamless…

10395 Haupt

Soma Cube

7 pieces = 1 cube. Each of the seven components of this large cube is a polycube. This means each piece consists of several small cubes. Spatial imagination…

10345 Detail

Square Puzzle and the Square to Triangle-Conversion

Disassemble and reassemble – discrete geometry. Square puzzle: Nine square tiles of different sizes. Arranged correctly, they fit into an almost-square…

10448 Haupt

T-Puzzle

Frustratingly simple. Four pieces make up a puzzle. When placed correctly, they form the letter T. Child’s play. But: is this task really that easy?

10237 Haupt

Template Code

Untangling the letter jumble. Perfectly possible, with the right template. Using it in reverse, you can encrypt a 36-letter message, almost impossible for…

10437 Haupt

Tetrahedron Puzzle I

Three-sided pyramid, puzzle with two pieces. Spatial imagination is required: when correctly combined, these two equally sized bodies form a…

10438 Haupt

Tetrahedron Puzzle II

Three-sided pyramid, puzzle with four pieces. Spatial imagination is required: when correctly combined, these four equally sized bodies form a…

10439 Haupt

Tetrahedron Puzzle III

This puzzle game is mainly about spatial imagination. Four (2 equal) bodies made of spheres are to be assembled to form a tetrahedron.

10071 Haupt

Th shortest Way is not always the quickest

Marble race. Three tracks with the same height difference and the same horizontal distance, but different curves: the straight path is the shortest,…

10338 Haupt

The Circle’s the Limit!

A circle with many corners. Reflect green laser light to form a triangle, a quadrilateral, a pentagon, a … The more corners this polygon has, the more it…

10120 Haupt

Thread Models

Straight threads, curved surfaces. Rotatable cylindrical model: a cylinder becomes a hyperboloid. A surface generated by the rotation of a hyperbola. Movable…

11473 Haupt

Three Balls on a String

Motion patterns with momentum. Three balls on a string: what pendulum motions occur at low, medium, and high rotation speeds? Depending on the rotation…

10451 Haupt

Towers of Hanoi

Rearranging – how many moves does it take? Five disks stacked on a pole, arranged from largest to smallest. These five disks need to be moved to one of the…

10495 Phänomen

Water Parabola

Parabola in a natural phenomenon. As the rotational speed of this container increases, the water surface inside curves. The faster it rotates, the steeper the…

10161 Haupt

Weird Wheels

Not round, but it rolls round. These discs aren’t round, but when they roll, their axis stays at the same height: solids of constant width. Disc-shaped bodies…

10482 Haupt I

Wobbly Bridge I Arch Bridge / Wobbly Bridge II Suspension Bridge

Suspension bridge – an arch bridge viewed from a different angle and subjected to a different load. Resembling a suspension bridge, the chain bridge reflects…

10519 Haupt

Wolf, Goat and Cabbage

Keep calm, ferryman! Task: transport cabbage, goat, and wolf to the other side of the river. Tricky, since only one other passenger fits on the ferry. The…

10144 Haupt

Your Birthday in Pi

Ten million decimal places. Somewhere in π lies your birthday or your license plate number. This computer station can find any six-digit combination. At…

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Mathematics