NUIM MathSoc
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If you want to learn how to code in Scilab (the free alternative to MATLAB) you may have a look at this page that contains several free tutorials.﻿
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Snowflakes are amazingly diverse!  The first scientific classification of them goes back to Ukichiro Nakaya. Trained as a nuclear physicist, in 1932. Nakaya was appointed to a professorship in Hokkaido, in the north of Japan. There were no facilities to do nuclear research, so Nakaya turned his attention to snowflakes!  Besides studying natural snow, he created artificial snowflakes, and figured out which kinds form in which conditions.  In 1954 he summarized his work in a book, Snow Crystals: Natural and Artificial.  This is his classification.

For more on the history of snowflakes, and amazing photos of them, see Kenneth Libbrecht's page:

http://www.its.caltech.edu/~atomic/snowcrystals/earlyobs/earlyobs.htm﻿
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Why are there just five platonic solids (and what are platonic solids!?)

The solids are the tetrahedron, hexahedron (cube), octahedron, icosahedron and dodecahedron.﻿
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Everything you see is made of smaller things with the same shape.  created this striking image by writing out complex numbers in base –1+i and coloring the plane according to the 'digits' of these numbers.   The fractal curve you see all over here is called the twindragon.

In 1964, S. I. Khelmenik wrote a paper in the Russian journal Questions of Radio Electronics in which he showed that every complex number can be uniquely expressed as a string of bits with a decimal point in it, like

1011001.1101010101000000101001100111101011000010101...

if we work in base –1+i.   This was rediscovered by Walter F. Penney in 1965, later by other people, and popularized by Donald Knuth in vol. 2 of The Art of Computer Programming.  For more on these see:

http://en.wikipedia.org/wiki/Complex_base_systems

has a great page of mathematical images, from which I took this picture:

http://bendwavy.org/doodle/﻿
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A sort of sieve of Erastosthenes implemented with rotating annuli. Pretty cute! It'd be nice if it made a bigger deal when one got to highly composite numbers. Try spinning it really fast, then rotating backwards through 0.﻿
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Vi Hartoween!  ﻿
's Halloween Video! ﻿
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Cool podcast!﻿

Paul Erdos was one of the greatest mathematicians of the 20th Century, the one that other mathematicians measure their distance from, and beyond that one of the most interesting. His highly collaborative, highly nomadic life brought him in touch with hundreds if not thousands of other mathematicians, and every single on of them has their own Erdos story to tell. In order to find out more about the man, Samuel Hansen spoke to three of his collaborators and the man who runs the Erdos Number Project.

http://relprime.com/erdos/﻿
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Ever feel like you aren't making any progress?  This video is amazing in its ability to combine a sense of motion and a sense of not going anywhere.  It's by Vladimir Bulatov.  It's based on Escher's woodblock Circle Limit III:

"Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's wood engravings Circle Limit I–IV demonstrate this concept. In 1959, Coxeter published his finding that these works were extraordinarily accurate: "Escher got it absolutely right to the millimeter.""

But it also uses Bulatov's own work on conformal geometry:

http://bulatov.org/math/1001/

The quote is from:

http://en.wikipedia.org/wiki/M._C._Escher#Works

Here's a video of Coxeter talking about Escher's Circle Limit series:

Coxeter discusses the math behind Escher's circle limit

#sciencesunday  ﻿