Geometry and Topology

Swallowtail on the shore

Submitted by IMAGINARY on Sat, 09/06/2014 - 15:56

Platonic solids, Felix Klein, H. S. M. Coxeter and a flap of a swallowtail: The five Platonic solids tetrahedron, cube, octahedron, icosahedron and dodecahedron have always attracted much curiosity from mathematicians, not only for their sheer beauty but also because of their many symmetry properties. In this snapshot we will start from these symmetries, move on to groups, singularities, and finally find the connection between a tetrahedron and a “swallowtail”.

Minimizing energy

Submitted by IMAGINARY on Wed, 07/02/2014 - 22:01

What is the most efficient way to fence land when you’ve only got so many metres of fence? Or, to put it differently, what is the largest area bounded by a simple closed planar curve of fixed length?
We consider the answer to this question and others like it, making note of recent results in the same spirit.

Arrangements of lines

Submitted by IMAGINARY on Tue, 07/01/2014 - 17:50

We discuss certain open problems in the context of arrangements of lines in the plane.

Billiards and flat surfaces

Submitted by IMAGINARY on Fri, 06/06/2014 - 19:45

Billiards, the study of a ball bouncing around on a table, is a rich area of current mathematical research. We discuss questions and results on billiards, and on the related topic of flat surfaces.

Matrixfaktorisierungen

Submitted by IMAGINARY on Fri, 02/21/2014 - 18:43

Im Folgenden soll ein kurzer Abriss des Themas Matrixfaktorisierungen gegeben werden. Wir werden darlegen, warum dieses recht simple Konzept zu erstaunlich tiefen mathematischen Gedankengängen führt und auch in der modernen theoretischen Physik wichtige Anwendungen hat.

Geraden, Kurven und Kuspen

Submitted by IMAGINARY on Wed, 09/04/2013 - 00:25

The algebraic geometer Duco van Straten, Johannes Gutenberg-University Mainz, Germany gives a beautiful short introduction into the field of algebraic geometry - from lines, curves to cusps. It shows many pictures and also links its content to historical events and applications.

Martmatics

Submitted by IMAGINARY on Mon, 06/24/2013 - 00:47

Martmatics is a project to show how Mathematics and Art have been related to each other throughout history and how they are still linked today. There are many bonds and the authors have chosen the most attractive and significant ones. You will find a brochure and also an activity book with excercices to accompany the examples from the brochure.

IMAGINARY Worksheets for Schools

Submitted by IMAGINARY on Tue, 03/19/2013 - 15:27

A collection of IMAGINARY worksheets for school children. The worksheets are of different levels of difficulty, aimed at children and teenagers aged between 5 and 17 years. The material has been developed for the IMAGINARY exhibitions in Spain and was awarded with a prize of the Initiative “Ciencia en Acción” 2012.

School Taskbook: From 5 to 15

Submitted by IMAGINARY on Sat, 02/23/2013 - 12:19

The taskbook for school students by renowned Russian mathematician Prof. Vladimir Igorevich Arnold. You can find the original Russian version as well as an English, German, Spanish, Italian, Vietnamese and Turkish translation.

If you are interested to add a new translation, please see the github repository of the booklet for all sources and details.

Didactical Guide Bilbao

Submitted by IMAGINARY on Sat, 02/23/2013 - 12:18

Didactical guide to the IMAGINARY exhibition

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