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Re: [Phys-l] Infinite recursion, iterated maps, ...



On 04/19/2011 06:57 AM, Herbert Schulz wrote:
Imagine making a vertical cut to the right of the first R3.

Right.

================

It is worth thinking about the _idea_ behind this method of solution,
because the idea comes up again and again. Indeed this idea is
closely related to the very definition of infinity.

Here's a non-electrical purely-mathematical example. R is
defined by in infinitely recursive formula

R = crt(6 + crt(6 + crt(6 + crt(6 + ...)))) [A]

where crt stands for cube root.

Equation [A] or one of its congeners tends to show up on the high
school math contest every year. The algebra is dead simple; the
only challenge is to understand what "..." means.

Another word for this type of problem is "iterated map". The value R
is a "fixed point". Iterated maps show up a lot in physics, including
dynamics, including chaotic dynamics.