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Mathematics

Exhibit-Links
11976 Phänomen

847 Compass needles

Magnetic Domains. There are 847 compass needles attached to a disc. Because they are so close together, they influence each other. With a magnet, the compass…

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,…

11364 1

Ball sorting machine

Playful tidying up. Yellow. Red. Blue. This machine sorts the small, medium, and large balls among Pierre Andrès' “Machines Singulières” in a playful manner.…

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…

10207 1

Bouncing (Steel) Ball

Ping-ping, not ping-pong. When a ping-pong ball drops onto the table, its sound is unmistakable. A tapping noise that grows quicker and quicker. This happens…

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…

10484 1

Convection cells

«Convection Cells» Warm air rises, as does warm liquid. This forces air and moisture to descend in other areas. The structures that form resemble cauliflower…

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…

Digitale Sonnenuhr stand

Digital Sundial

"Digital" sundial. It casts no shadow. Instead, it displays the time using illuminated numbers—without any electronics. A combination of aesthetics and…

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…

11477 Haupt

Distorted Room (Ames Room)

Little one grows tall. An absolutely ordinary room, at least when viewed through the peephole. But wait, the little brother grows taller than the big sister…

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…

11978 Hauot

Emotion detector

Measuring skin resistance. The skin resistance is influenced by the subject's emotions: the stronger the emotions, the lower the resistance. Here, the skin…

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,…

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…

11974 Detail

Generator track

A magnet generates electric current. A track with a magnetic toy railway on it runs through a large coil. When the toy track is moved in the coil, a current…

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…

10166 Gravitationsmodell oder Der Potetialtopf Haupt

Gravitational model or Energy Well

The potential well. Orbiting the gravitational center: once launched, the ball takes wide rounds. For minutes, it gradually accelerates. Its circles become…

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…

11823 Haupt

Jumping Water

Fascinating Water Arches. Is solid water flying through the air? Beautiful: sometimes, continuous arches form, almost like tent poles, but made of water.…

10220 Haupt

Kalliroscope©

Magic and Beauty of Flowing Motion A vortex generator or rather a spectator par excellence. It allows for enchanting, seemingly chaotic, yet somehow regular…

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…

10422 Detail

Liquid Dynamics

Chaotic eddies, turbulent swirls – and calm zones. Turbulences become visible. In the flow tank, they appear in the water. Very similar to what happens in a…

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…

10254 Detail

Lying Water Disk

Water shapes sculptures. When two water jets collide, the water is deflected sideways. A water membrane forms, creating a disc. The pressure in the two pipes…

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…

11117 1

Magic Wave

A mechanical work of art: A rhythmic rise and fall of metal segments, reminiscent of traveling waves. With a remarkable setup, the artist induces phenomenal…

11118 1

Magic Wave Model

Magical wave in the stairwell – principle clearly explained. A rotating arm, cords, guide points, and straight metal segments create a wave-like motion that…

11701 1

Mirror cubes

Create different figures with coloured wooden blocks and on a mirror surface. What does the built cube world look like mirrored several times?

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…

10310 1

Pendulum Wave

Chaos in perfect alignment. Eleven pendulums of different lengths. Once released, they swing in disarray. And yet, every ten seconds, they return to perfect…

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…

11104 Illustration alt

Quick thinking

The moment of shock in road traffic - not just a simple reaction but also thinking! Unlike the simple reaction time, this also involves thinking quickly:…

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…

10360 Haupt

Sand images

Sliding, floating, flowing So beautiful, so fascinating: The sand, moving here between glass plates, tells a story far beyond that of an hourglass. When it…

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…

11331 1

Shepherd’s Sundial

North? Not relevant. A simple sundial, like those used by shepherds for centuries. The advantage of this clock is that knowing the north direction is…

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…

11818 Phänomen I

Squaring the Circle

Everything always has two sides. From one side, it looks like a square; from the other, a circle. It’s all a matter of viewpoint and perspective. The…

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,…

11864 Haupt

The big is in the small: crystals

Amazing Order Shake it, please. When the balls come to rest, they arrange themselves into regular patterns. These patterns can be compacted, almost to…

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…

11944 Haupt

The finest difference

How fine is your dexterity? Very fine: experience how this is defined for you with this exhibit. You can feel when something sticks out by ten millimeters.…

DSCF1135

The Tea Leaves Experiment / Tea Cup Experiment

«Everyday Physics» Experiment like Albert Einstein. In a paper about river meander formation, he wrote: «I begin with a small experiment that anyone can…

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…

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…

10975 Haupt

Watch Water Freeze / Ice Flowers

Watch Water Freeze Crystals form on the cold surface, like frost flowers on windows, a sight we see less often thanks to better insulation. Here, you can see…

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…

11328 1

Wind Machine

Breeze, storm, hurricane. From a gentle breeze to a raging storm: play with the wind. Reduce your surface area or expose as much of it as possible to the…

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…

Experiment-Links
Agar Cell Diffusion DSC 0413 P960

Agar Cell Diffusion

Use cubes of agar to investigate how size impacts diffusion. All biological cells require the transport of materials across the plasma membrane into and out of…

Anti Gravity Mirror DSC 6663 H1

Anti-Gravity Mirror

Learn how to fly with this neat mirror trick. A reflection of your right side can appear to be your left side. Try this activity and you'll appear to perform…

Life Size Main

Life Size

Explore the size and scale of microscopic biology. Not only is it hard to conceptualize things that are too small to see, it’s often surprising to discover the…

Workshop-Links
DSF4159

Asseln unter der Lupe - inklusiv

Asseln sind bestimmt keine besonders beliebten Haustiere – umso mehr eignen sie sich aber als Einstieg in die Tierkunde. Was machen eigentlich Zoologen, deren…

Spurensicherung expo

CSI Technorama – forensics

Regardless of whether it is a burglary, an accident or a felony, crime scene investigations always begin with securing the evidence. Are there fingerprints?…

Iss

Happy hour on the ISS – water purification

Even astronauts on the International Space Station ISS enjoy drinking a Campari Soda from time to time – but where do they get the soda water from? There is no…

Fluoreszenz2

Lighting effects in nature and the home – fluorescence

How can you light up fluorescent objects? Where do lighting effects occur? You extract fluorescent dyes from everyday objects like pudding mixes or laundry…

Strahlende Einsichten

Radiant insights – radioactivity

CERN in Geneva, the catastrophe in Fukushima, new radiotherapies for treating cancer – atomic and nuclear physics are constantly discovering new findings that…

Asseln

The beauty in the beast – scientific methods

It is safe to say that isopoda (woodlice) are not the most popular pets – but they are all the more useful for zoology. What do zoologists actually do when…

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Acoustics

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Aggregate states

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Algorithms

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Animals, plants, habitats

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Atomic and quantum physics

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Atomic structure

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Automats

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Biology

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Buoyancy

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Chaos

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Characteristics of life

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Chemical Reactions

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Chemistry

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Colors

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Computer science

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Cryptology

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Currents

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Data and information

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Design elements

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Earth sciences

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Electricity

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Electricity and energy

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Electricity and magnetism

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Elektromagnetismus