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Tuesday, September 24, 2013

Reading Challenge: The Road to Reality

The Road to Reality. A complete guide to the laws of the universe.

Prior to my more serious interests in Mathematics I challenged myself to read Goedel, Escher, Bach. Not an easy task if you aren't familiar with musical theory at all. It took me about six months to complete the book. Of course I was in doubt if I really understood it all ( I didn't, not sure if I do know, even after M381 Mathematical Logic, but math grows on you ). Anyway, I have been told that The Road to Reality by Roger Penrose is a book of similar importance as GEB. With it's 1100+ pages it's a challenge alright.

I intend to read it while commuting. Who says commute time can't be made productive? Clearly this is a self-motivating post ;-), but an announcement of a log as well. Sort of a summary of the book in parts. More later. I completed one chapter sofar or 25 pages which is less than 3%.

The Big LaTeX discussion

Although it is perfectly acceptable to handwrite your TMAs at the beginning of every course someone starts the "Big Latex Discussion" again.

It's usually a nerd that starts off by listing the irrelevant but impressive specs of his ( not often her ) hardware, or bloats how much computing know how he has ( part-time math students often work in IT ). He then announces that he 'is going to make his TMAs in LaTeX.

Wow. Jaws dropping. Not.

Not often he also provides us with a list of software artefacts required, version numbers included. Nerdy but deep in the autistic spectrum.

I haven't decided how I'll produce my TMAs this time. I see three options. Hand-written, LaTeX typeset or (new!) handwritten but digitally stored in vector graphics format.

LaTeX became a problem ( pita ) for me in the past when I had to add drawings and stuff. Making and including mathematical drawings in LaTeX is not trivial. Besides it is a major distraction, while you should be thinking about math you are figuring out how some latex drawing package works. Serious waste of time.

Since you can draw on a tablet, store it in SVG and thus manipulate it any way you want, doing the formulas in LaTeX and the drawings 'by hand' is probably the route I take.

Since I do Android work Eclipse became more or less my IDE of (only) choice so I'll give TeXlipse with PDF4Eclipse a try.

Tuesday, September 17, 2013

Tilings resources

I am on a OU course again, ( more about that in posts to follow ). The course site opened today, that really kicks off the course for me.

For now some resources you might find interesting.

A tiling is a covering of the whole plane with non-overlapping tiles, each of which is a topological disc. The classic work on tilings is Tilings and Patterns by Grunbaum, Shephard. A list with other books on the subject can be found here.

M.C. Escher used tilings in his graphics work in an ingenious way. This book contains a nice collection of the work of Escher.

It's interesting to note that in Escher's time (1901-1972) there was hardly any mathematical theory about tilings. The foundational work on tilings was published five years after Escher died. Yet from Escher's work it is clear that he understood tilings, and the related line symmetries ( Frieze Patterns ), lattices and plane symmetries ( Wallpaper Patterns ) as no other.

If you are interested in puzzles at all it's likely that you came across Jaap's Puzzle Page, a vast resource of information regarding puzzles. The website is maintained by Jaap Scherphuis. You'll find his YouTube site here with many puzzle demonstrations.

To my astonishment Scherphuizen also maintains an impressive collection of tilings on a Tilings Page. His tilings demonstrations Java Applet is as impressive which you'll find on the same page.

'Pentagon Flower' ( background tiling is the [4,8,8] Laves tiling )
(c) nilo de roock 2012

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Mathematics: is it the fabric of MEST?
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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.)