and I got my birthday present (my wife is awesome) up on the wall in my office this morning :) It looks pretty amazing :)
Here is the post the ol' (hot, beautiful, clever and kind) ball and chain put up with pictures of me opening it: http://goo.gl/lccZ6N
If you're unfamiliar with Thomas's work I recommend going to check it out.
The number pi or π, (approximately 3.14159265) is one of the most important quantities in mathematics. It is perhaps best known in the context of circles: a circle of diameter 1 has circumference equal to π.
This picture, created by Cristian Ilies Vasile, is a graphical representation of the first 10,000 digits of π. Each segment represents a digit from 0 to 9, and within each segment, there are 10,000 positions, one for each digit of π being represented. We write “m:n” as shorthand for “position n of segment m”.
Each of the coloured strands represents a link between two successive digits, so the first two digits of π (3 and 1) are represented by a strand from 3:0 to 1:1; in other words, from position 0 of segment 3 to position 1 of segment 1. The sequence of coloured strands continues according to the sequence 3:0 → 1:1 → 4:2 → 1:3 → 5:4 ...
The sequence of digits of π never terminates and never goes into an endlessly repeating loop. This is because π is an irrational number, which means that it cannot be expressed exactly as a fraction. Sometimes people say that π is equal to 22/7, but this is merely a convenient approximation.
In some sense, π is “more irrational” than numbers such as the golden ratio (approximately 1.618): although neither number is equal to a fraction, the golden ratio is a root of the polynomial x^2 - x - 1, whereas π is not a root of any polynomial with integer coefficients. Mathematicians express this by saying that the golden ratio is an algebraic number, whereas π is a transcendental number.
The upshot of this is that the digits of π are more or less random. However, there is a sequence of six consecutive 9s, called the Feynman point after physicist Richard Feynman, which appears after only 762 decimal places. Feynman once stated during a lecture that he would like to memorise the digits of π until that point, so he could recite them and quip “nine nine nine nine nine nine and so on”, thus implying that π was rational. (“Surely you're joking, Mr Feynman.”)
There is a lot more fascinating π artwork on Martin Krzywinski's web site (http://mkweb.bcgsc.ca/pi/art/). Thanks to for telling me about this picture!
This animation looks to me like a collection of hexagons of red dots, rotating and exchanging partners in a dance-like formation. The impression is given that each individual red dot will, over time, travel a significant distance around the picture, but if you focus on one dot, you'll see that this is not the case at all!
I found the animation on mathmunch.org (http://mathmunch.org/2013/10/10/tsoro-yematatu-fanos-plane-and-gifs/#comments). The aim of the site is to post three great finds each week from the mathematical internet, and their content looks very interesting.
The mathmunch site attributes the animation to David Whyte and Brian Fitzpatrick, who maintain a tumblr site called Bees & Bombs (http://beesandbombs.tumblr.com/). The latter site contains a great variety of animations of a similar nature.
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