A piece of pi

A piece of pi

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 Skip Jimroo for telling me about this picture!

#mathematics  #sciencesunday

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19 Comments


  1. Unfortunately, all the myths and blah blah go with it. But it gives curves and proportions that procure emotions and sensuality. That the only important thing to take in consideration (You certainly know what I mean, because you know what they reffer to)

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  2. Sergio Ricardo de Freitas Oliveira Their inner structure is made apparent. There are no true random numbers or series anywhere in the universe. They all have a pattern. See my post about this graphic for more information.

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  3. Sergio Ricardo de Freitas Oliveira I’m aware of these tests. Statistics is only about the attributes and relations of a distribution. Distributions are the domains I’m referring to. There is no randomness. Really!

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