Thursday, January 27, 2011

Deep meaning in Ramanujan's 'simple' pattern - physics-math - 27 January 2011 - New Scientist

Deep meaning in Ramanujan's 'simple' pattern: "They found 'fractal' relationships in sequences of partition numbers of integers that were generated using a formula containing a prime number. For example, in a sequence generated from 13, all the partition numbers are divisible by 13, but zoom in and you will find a sub-sequence of numbers that are divisible by 132, a further sequence divisible by 133 and so on."
Ono's team were able to measure the extent of this fractal behaviour in any sequence; Ramanujan's numbers are the only ones with none at all. That may be what he meant by simple properties, says Ono...
Trevor Wooley, a mathematician at the University of Bristol, UK, cautions that the use of the term "fractal" to describe what Ono's team found is more mathematical metaphor than precise description. "It's a word which conveys some of the sense of what's going on," he says.

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