As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

## Saturday, March 31, 2012

### What is a lattice? - Or lattices in M336

#openuniversity #m336

The Open University course M336 contains two booklets which are dedicated to lattices. One booklet about two-dimensional lattices (GE3) and one about three-dimensional lattices ( and polyhedra ) (GE6). To a layman I would explain lattice as some regular grid of points ( connected by thin lines ).

 Click to enlarge

In the example above the lattice is defined by two vectors and consists of all points $n \mathbf{a} + m \mathbf{b}$ where $n,m$ are integers.

Fields which use lattice theory are crystallography, finance, game ( maze ) programming, group theory and number theory. When I dug a little bit deeper I discovered that the field of lattices is -ginormous-. Gabriele Nebe and Neil Sloan ( yes him ) maintain a catalog of lattices which now contains over 160,000 lattices. Mathematicians like to generalize over n-dimensions so yes, that database contains lattices in dimensions higher than 3. Like lattices in 40 dimensions for example. Forty.

A catologue of lattices.
Junkyard article about lattices and geometry of numbers.

The mathematical universe is expanding with tremendous speed.

## Wednesday, March 21, 2012

### M336 - Group Theory - Fundamental Theorem of Abelian Groups

#openuniversity #m336 #video

One of the theorems that is discussed in the group theory track in the Open University Course 'M336 Groups and Geometry' is the Fundamental Theorem of Abelian Groups. Early on in Group Theory it becomes clear that there is a connection between group theory and number theory in Langrange's theorem and the Sylow Theorems ( also part of M336 ) but only after studying the Fundamental Theorem of Abelian Groups you'll get a notion of the depth of the connection between Group Theory and Number Theory.

MathDoctorBob ( his YouTube alias ) made a short video lecture on the topic. Precise as always.

## Sunday, March 18, 2012

### Frieze Patterns and Conway

#mathematica #m336 #openuniversity

John Horton Conway (26 December 1937 - ) is a prolific mathematician who contributed to many branches of mathematics. He is the inventor of the cellular automaton "Game of Life". He is currently Professor at Princeton University. He added yet another set of names to the Frieze Patterns. Since they are not mentioned in the M336 course booklet I suppose the names weren't adopted widely enough.

Conway proposed the following names for the seven frieze patterns:
- Hop for p111, translational ( only ).
- Sidle for pm11, vertical.
- Jump for p1m1, horizontal.
- Step for p1a1, glide.
- Spinning hop for p112 rotational.
- Spinning jump for pmm2 horizontal and vertical.
- Spinning sidle for pma2 vertical glide.

 Click to enlarge

## Friday, March 16, 2012

### M336 - Progress

#math #maths #OpenUniversity #M336 #Escher

Today I had "the click" on 2-dimensional lattices ( M336 - GE3 ). Let me show you some output of my M336 Mathematica notes.

The top-left part of the image is a building block from which, for example, a frieze or a lattice is constructed. The image, or the plane, of the building block is deformed by two vectors such that a new shape is created. The lower part of the image is a 4-by-5 lattice of a deformed copy of the image above.

Before I started M336 I rather looked up to studying the 17 Wallpaper Groups. Mainly because I thought they were no fun, boring. And now that I am close to studying them in GE4, I can't wait. I hope to be able to computer-generate some of Escher's art with the program I made. But more about that another time, but soon.

### hELP !

#openuniversity

Stop the cuts in the Open University

Thank you very much.

( You must be a British citizen or normally live in the UK to create or sign e-petitions. )

## Wednesday, March 14, 2012

### Happy Pi Day

If you haven't seen =the= classic mathematics movie yet: Pi, do so today. It has a 7/5/10 rating from 76K+ users on IMDB, what more can I add?

Because it's Pi day:

The following proof is simple. = Therefore I provide only the shortest possible and encrypted version of it.

This text is self contained. = The reader is assumed to have a Ph.D. in the field.

Notation. = To disguise the fact that most of this work is copied from the standard text in this subject I have used a different notation.

The last one may seem cynical but the amount of ( literal ) overlap in mathematics books is noteworthy.

## Tuesday, March 13, 2012

### Publishers - Continued

From a forum who SWIM regularly visits:

Last Thursday, I purchased an international version of a textbook for a course that I'm about to take. The list price is USD 233.33. Amazon has it for USD 180.40. That's a lot of money. After shopping around online, I found it for USD 48.98, shipped, which was the version that I bought. I sent that amount through PayPal to the seller, who appears to be in Hong Kong, although the book, itself, came from Germany.

When the book arrived, I found the following sidebar on the back cover:

This is a special edition of an established title widely used by colleges and universities throughout the world. Pearson published this exclusive edition for the benefit of students outside the United States and Canada. If you purchased this book within the United States of Canada you should be aware that it has been imported without the approval of the Publisher or the Author.

Person International Edition

There are three aspects to this note that are interesting. First, only barristers would capitalise 'publisher' and 'author'. That's the way that it's done in legal agreements (i.e. contracts). Second, how is an 'exclusive edition' with the identical text beneficial to students outside, but not inside, the United States and Canada? What, exactly, is the nature of this 'exclusive' edition that gives it such a remarkable property? Perhaps it's that this version is softcover, as opposed to hardcover. However, frankly, I don't feel like paying USD140 more for a hardcover book. Third, what is the significance of the importation of this 'exclusive' edition not being approved by the publisher or author? Pearson seem to be saying, 'You may think that you're getting away with it, but we are going to track you down, sue your arse, and take your money by force, thief!'

 Fermat

## 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.)