# The Magical Maze: Seeing the World Through Mathematical Eyes by Ian Stewart

By Ian Stewart

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Additional info for The Magical Maze: Seeing the World Through Mathematical Eyes

Example text

Again, our aim is not so much to hack our way to a solution, as to argue our way towards a general method. Mathematicians have a catch phrase for this trick: 'let 2 n'. Anyone can specialise from the general to the particular ('let n = 2'); the true art of the mathematician is to go the other way, and generalise an idea from a particular case to all of them. By learning to navigate their way through small but representative parts of the magical maze, mathematicians often find out how to fight their way through the whole thing.

More recent work still, by the French physicists Yves Couder and Stefan Douady, has shown that this choice of angle is a natural consequence of the dynamics of a growing plant shoot . Each new primordium gets pushed into the biggest space available. That means that they all pack together efficiently, and that in turn implies that the golden angle is the most likely choice. , which was widely known to be the next most common sequence of numbers chosen by flowers. So the theory explains the exceptions, as well as the more common Fibonacci numbers.

11 n 11 n n n 112 - - 3 12 Figure 17 Typical moves in 3-disc Hanoi. 231 Panthers Don't Like Porridge 55 This is on needle 2, and corresponds to the first occurrence of 2 in the sequence. Suppose we change this first 2 to 1. ) the first occurrence of the digit 1; so the move from 212 to 112 is legal. So is 212 to 312, because now the first occurrence of 3 is in the first place in the sequence. We may also move disc 2, because the first occurrence of the symbol 1 is in the second place in the sequence.