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?
Explore how we can represent the notes in a logical and useful way! The Tonnetz is a pictorial representation of the notes in the plane that reveal affinities and structures between notes and on concrete music pieces.
Explore the science of cartography and the geometry of map projections.
Circular shaped mirrors which are arranged in a grid-like manner reflect a light ray according to the reflection law of geometric optics. While random positions of the light source produce chaotic reflection patterns, it is possible to position the light source so that beautiful symmetric reflection patterns are created.
The application allows you to interactively change parameters like light source position, circle radius and rotation angle of the lattice. Through a simple menu it is possible to select and explore a wide range of symmetric reflection patterns.
This exhibit explores the science of cartography and the geometry of the sphere. The geometric properties of the sphere and the plane are essentially different, and no map can faithfully represent the Earth without distortion. This module goes through some of these properties, comparing different map projections and trying to get a feeling of what “distortion” means and why is there such impossibility for a “perfect map”.
Experience this interactive program and fly through a quartz, fluorite, or diamond crystal. You can steer a miniature spaceship through the crystal structures using your finger on a touchscreen, also in 3D.
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 images, multiple layers of images and animations. Additionally it contains a series of sample galleries with explanations.
SURFER 2008 is the original Surfer version that was developed for the IMAGINARY exhibitions in the Year of Mathematics 2008 in Germany.
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 surfaces in space. Mathematically, the program visualizes real algebraic geometry in real-time. The surfaces shown are given by the zero set of a polynomial equation in 3 variables. The letters/words are transformed into algebraic equations.
