Exhibitions

Jos Leys, Étienne Ghys and Aurélien Alvarez

Submitted by IMAGINARY on Wed, 08/29/2012 - 00:08

The following pictures are images from two chapters of the film “Dimensions, a walk through mathematics” rendered in high-resolution. In one chapter, Hipparchus shows us how to describe the position of any point on Earth with two numbers and explains the stereographic projection. In another chapter, mathematician Ludwig Schläfli talks about objects that live in the fourth dimension, and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces! Two pictures of the exhibition that look like knots are special.

Ulrich Pinkall, Nicholas Schmitt, Charles Gunn and Tim Hoffmann

Submitted by IMAGINARY on Tue, 08/28/2012 - 23:19

Differential geometry is the study of curved shapes, like curved lines or surfaces in space, or even shapes with many dimensions. From the viewpoint of differential geometry the shapes of soap films and soap bubbles are singled out by the fact that the so-called “mean curvature” is the same at every point of the surface. Several pictures in this gallery show surfaces of constant mean curvature, one picture shows a surface that does not have minimal area but minimal “total curvature”. Another picture shows a three dimensional space of constant curvature.

Richard Palais and Luc Benard

Submitted by IMAGINARY on Tue, 08/28/2012 - 00:39

The paradigm changing modern technology of computers has provided spectacular new possibilities for visualizing ever more complex mathematical objects and processes. The authors of this gallery explore these objects, using among others 3D-XplorMath,

Morenaments

With Morenaments you can easily paint symmetrical patterns in one of the 17 symmetry groups of the Euclidean space. Discover geometrical properties and investigate their inner structure of spinning centers and mirror axes. Or feel free to paint in a creative way and experience how a few strokes fill the entire space in a beautiful ornament.

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SURFER

With SURFER you can experience the relation between formulas and forms, i. e. mathematics and art, in an interactive way. You can enter simple equations that produce beautiful images, which are surfaces in space. SURFER is the Java-based extension of the program SURFER2008 that was developed for the IMAGINARY exhibition in the year of Mathematics in Germany.

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IMAGINARY

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Jos Leys, Étienne Ghys and Aurélien Alvarez

Ulrich Pinkall, Nicholas Schmitt, Charles Gunn and Tim Hoffmann

Richard Palais and Luc Benard

Morenaments

SURFER

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