Remember that the problem was to find the equivalent resistance of this thing with :

.

We know the equivalent resistance must exist, because it can’t be less than zero, and every time we add more resistors in series the resistance decreases, so we have a bounded monotonic series.

Replacing the back part of the circuit with its equivalent resistance, we get a diagram like this:

Now find the equivalent resistance to .

which simplifies to

,

which is the golden ratio.

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July 18, 2011 at 12:44 pm

[…] This is a famous problem, solved many places online. I wrote a solution here. […]