This problem was aired previously by Steve Witham just before Christmas 2007; or rather, its rather tougher relation where the nodes are one knight's move apart. I think the subject line might have been "xkcd points out dangers of math fun" ? I shan't spoil it for newcomers; but possess a record of the thread for anyone requiring a crib! WFL On 2/12/14, Tom Karzes <karzes@sonic.net> wrote:
This reminds me of an old puzzle:
You have an infinite square grid of 1 ohm resistors. What is the resistance between two adjacent nodes in the grid?
More precisely, you have an infinte square grid of nodes. Each horizontally adjacent pair of nodes is joined by a 1 ohm resistor, and each vertically adjacent pair of nodes is joined by a 1 ohm resistor. What is the resistance between two adjacent nodes (either horizontal or vertical)?
Tom
Richard E. Howard writes:
The most fun paper in this field (in my opinion) is by Last and Thouless in 1971.
In this era of Higgs Boson-sized experimental budget, it is a study in elegance. They punched carefully randomized holes in carbon paper (2D conducting sheet) and measured the resistivity as a function of hole density.
The experiment trumped the theory at the time and the apparatus (for once) actually cost less than the pencil/paper theory...
--R
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