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## Tuesday, March 6, 2012

### Explorations beyond M336: the permutohedron

#maths #openuniversity

M336 is a two track level 3 Open University Mathematics Course with geometry track covering frieze- and wallpaper patterns, tilings and polyhedra, and a group theory track covering the Correspondence Theorem, the Sylow Theorems and the classification of Abelian groups. - When you are doing a course you are not only learning the course materials but it also broadens your view on the field. Well, I have seen quite a few new and ( fascinating ) topics lately.

Two short ones in this post and more to follow.

If you are into mathematics I bet that you have seen Inception, not that it is a mathematics movie per se but it is the type of movie math geeks love, I am sure. Anyway, do you remember the scene where Cobb and Ariadne walk on the Seine boulevard where she turns a mirror around and suddenly you see an infinite number of images. There is a name for the symmetry group of that pattern, it is a Dihedral Group with symbol $D_{\infty}$. Part of Group Theory is dedicated to studying that sort of groups, they are called Coxeter groups.

It took a while before I could dream the names of the five regular polyhedra: the tetrahedron, cube, octahedron, dodecahedron and isocahedron. But these are just the tip of the iceberg. There are enough familiar objects I don't know the name of. But there fascinating objects I never even heard of. Like the Permuatohedron for example: it is the n-dimensional generalization of a hexagon.

 Permutohedron

Exploring new territory in mathematics can be quite fascinating. A library ( brick and / or online ) is a good place to start.

## Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)