programs

Do you hear the climate crying? Data sonification makes changes happening on our planet audible. The numbers are not represented in tables or diagrams but in notes. Songs are created from them!

The Gulf Stream

The Gulf Stream is a current in the Atlantic Ocean that brings warmth from tropical waters to the coasts of northern Europe. As a result, temperatures are higher than in other regions similarly close to the Arctic.

Earth grid models

Even with the fastest supercomputers, we cannot fully model all climate processes in all regions of the world. Therefore, we divide the world into small grid cells and calculate the climate processes for these cells in parallel. The size of the cells is called the resolution of the grid. A...

Warming navigator

Explore the temperature trend

Box models

With a box model, we can predict the future by simulating the complex interactions between different processes. The results are often surprising, even though the connections between the processes are well-known and predictable.

Navier-Stokes equations

The movement of balls, cars, and rockets can be explained mathematically. Similarly, the Navier-Stokes equations can explain and predict the movement of fluids, like ocean water, atmosphere gases, an oil spill, smoke, or Currywurstsoße.

General Circulation Models (GCM)

General Circulation Models (GCM) are the most precise tool we have to assert that climate change is a reality. GCMs are detailed models of the whole Earth, divided into many small cells of just a few kilometers’ width.

Heuliad

Visualization of a family of sequences of points in a toric sub-lattice of the ring of Gaussian integers

Virtual Ray Tracer

Virtual Ray Tracer is a Unity application that visualizes ray tracing. The application shows a scene with a camera, lights and objects. Rays slowly shoot from the camera and interact with the lights and objects in the scene. Users can change the settings of the ray tracer and material properties...

Colorful Brownian Motion

With this web demo, you can play around with and learn something about Brownian Motion, a fundamental concept in the theory of stochastic processes and probabilistic physics.

The Chinese Remainder Clock

Discover and learn about the Chinese Remainder Theorem using clocks.

Surface Walker

A software to run around on the plane tesselated by the fundamental polygon of the torus or the Klein bottle. This is a alpha-version, feel free to improve it or use parts of the code to build your own!

Dirichlet Diagrams

A simple software to create “weighted Voronoi” or “Dirichlet” diagrams. Simple to use: Click to make a point, click again to start spread of colors, click again to stop spreading. Click on the “All” Button to start or stop all spreadings.

HyperRogue

HyperRogue — playing with hyperbolic geometry

Note Compass

Why is the music scale irregular? Why are there black and white keys in the piano, distributed in such a peculiar pattern? Why do we have a scale with tones and semitones? And more deeply, how notes are grouped into families, and what role do they play within such families?

The Harmonic Series #3 - 3D display

Sing into the microphone and move the synthesizer sliders to hear and see shifting chords.

KnotPortal

A VR software to explore knots through portals

Ariadne - Drawing Topology

Ariadne is a virtual learning environment about paths and homotopies designed for touch-capable devices.

Non-euclidean virtual reality

Virtual simulations of three-dimensional non-euclidean spaces, available at h3.hypernom.com and h2xe. hypernom.com

These are designed to work with the HTC Vive virtual reality system, on mobiles phones that have gyroscopes, and on...

Polygon App

Polygon is an interactive mobile app that allows users to discover polygons hidden in museums or science centers, and use them to construct Platonic and Archimedean solids. Scan polyhedra with your phone’s camera, answer mathematical questions to get powerups with additional shapes, and view the...

Rpolyhedra

Rpolyhedra is an R package with a polyhedra database and rendering capabilities with solid and net models

Powergrid Dynamics Simulation

Interactive simulation of power grid dynamics.

The mathematics of tides

Most people know something about what causes tides: if asked, almost everyone will say tides are caused by the moon. But if one delves a little deeper, it is easy to find many questions which arise naturally and are not so easy to answer. This interactive application tries to give an intuitive...

TsunamiLab

TsunamiLab is a web platfom that allows interactive simulation and visualization of tsunamis. It can be displayed as a normal website or as a hologram. Find more at tsunamilab.cl/hologram...

Fly faster? Fly shorter!

“Fly faster? Fly shorter!” is an educational math game (designed for one-player or two-players mode). Players fly a plane that cannot change speed, so they can win only by following the shortest route between the checkpoints they have to reach. But which is the shortest route on a map? Test your...

PyFWI - An interactive Software for the Simulation of Seismic Waves

The interactive software PyFWI demonstrates the propagation of seismic waves and the principles of seismic imaging.

Simulating the Melting of Ice Caps

Sea levels are rising for various reasons related to global warming. The glaciers of Antarctica and Greenland, known as ice caps or ice sheets, play a major role in sea level rise. Is it possible to predict future changes in these ice caps, and particularly the calving of icebergs into the ocean...

Dendritis

This module aims to educate young people (14-19) about the importance of trees, the significance of tree diseases worldwide, and their rates of infection. It introduces the concept of mathematical modelling, and attempts to demonstrate how an increasingly accurate mathematical model can be...

Interactive Traffic Simulation

Traffic and congestion phenomena belong to our everyday experience. In our simulation, you have the possibility to control traffic and create your own traffic jam. Find out how to trigger a traffic breakdown and how to resolve it. Observe how traffic jams can be seen as collective phenomena with...

Spacetime

Interactive simulation of the phase separation of two immiscible fluids.

Genaster

Genaster is a generalized asteroids game. The classic asteroids game glues the left screen edge with the right one and top edge with the bottom and therefore has a torus topology. This application considers other ways of gluing the screen edges.

GeCla

GeCla, short for Generator and Classifier, is a program for exploring the symmetries of of patterns/friezes or rosettes in the plane. GeCla allows you to generate a pattern, a frieze or a rosette with a previously chosen kind of symmetry starting from an asymmetric motif. It also allows the...

Random maps

The following 3d model is a simulation of a uniform random quadrangulation with 30 000 faces. You can think of it as follows. If you are given 30 000 rubber squares, you can stitch them together along their sides and obtain a surface homeomorphic to the sphere. In plain English, this means that...

Experimentarium Digitale

Experimentarium Digitale is a web site that makes available interactive numerical experiments of mathematical models in science and also a collection of augmented ebooks that bears the same name.

Der Tunnel von Samos

Beschreibung der Heron-Methode, die wahrscheinlich für den Bau des Tunnels von Samos benutzt wurde

Suzhi Kolangal/South Indian Traditional Art

In Tamilnadu, one would find a finest drawn and artistic drawing decorating every house at the front entrance.

These drawings are not just merely a decoration, but it has lot more significance to this practice.

During festival seasons and on any auspicious functions, the drawing...

Erdbeben und Strukturen

Jedes Jahr fordern Erdbeben auf der ganzen Welt viele Opfer. Während eines Erdbebens nehmen wir Vibrationen der Erdoberfläche wahr, die durch die Ausbreitung von seismischen Wellen entlang der Erdkruste entstehen. Die zentrale Frage, die wir in diesem Projekt beantworten wollen, ist: Welchen...

Karten der Erde

Dieses Programm beschäftigt sich mit Kartographie und der Geometrie der Sphäre. Die geometrischen Eigenschaften einer Sphäre und einer Ebene sind grundsätzlich verschieden, sodass keine Karte die Erde ohne Verzerrung abbilden kann. Dieses Modul behandelt einige dieser Eigenschaften und...

Patient Navigation Game

How can waiting times in the hospital be avoided to prevent criticism from patients?

Loxodrome und Spiralen

Dieses interaktive Modul illustriert (und definiert) Loxodrome und Spiralen auf der Erde, die außergewöhnliche Eigenschaften aufweisen, wenn man sie auf die Ebene projiziert, und setzt dies in einen historischen Kontext.

Calibration of Flood Models

To predict floods using three dimensional solutions of the Navier‐Stokes equations is completely impractical because of computation time and the large numbers of parameters that would need to be specified for such a model. The models which are actually used to predict flooding are so simplified...

Surfer Shuffle

Surfer Shuffle is an algebraic surfaces random generator based on the jsurf project.

SURFER 2008

With SURFER you can experience the relation between formulas and forms, i. e. mathematics and art, in an interactive way. SURFER 2008 is based on the Surf program and offers an intuitive user interface to create...

NameSurfer

With NameSurfer you can experience the relation between letters, words, formulas and forms, i. e. mathematics and art, in an interactive way. You can enter simple equations or words as for example your name. They will produce beautiful images, which are...

3D_XPLORMATH

3D_XPLORMATH ist ein extrem anschauliches und leicht verständliches Programm zum Erforschen der Mathematik. Unzählige Objekte, Animationen und Einstellungsmöglichkeiten laden die Benutzerinnen und Benutzer ein, sie mithilfe von 3D-Brillen zu entdecken!

jReality

jReality lässt die Benutzerinnen und Benutzer eintauchen in eine virtuelle Realität der Mathematik. Riesige mathematische Gebilde können erklettert und begangen werden, als ob sie real wären. Wie in einem Computerspiel kann man sich den verschiedenen Objekten mithilfe eines space navigators...

jsurf

jsurf is a Java based visualization library for algebraic surfaces.

Cinderella Applets

Important notice: Unfortunately the Cinderella applets no longer work „out of the box“. There are two alternative ways, though:

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