An obscure but interesting quantity of resistance.

Technically, surface resistance is a measurement of the amount of electrical resistance inherent in a coating of electrically resistive film on a nonconducting surface, such as the coating of chrome on a set of sunglasses.

What makes it interesting is the units: ohms per square. That is to say, a square piece of the material will always have the same amount of resistance, regardless of whether it is a one millimeter square or a 1 kilometer square. Thus, determining the resistance of a shape of the material is a matter of breaking the shape down into its component squares, then adding the equivalent resisters in series and parallel to get the resistance.

Thus, a piece of material with a surface resistance of one ohm per square that is shaped like this:

```    6
________
|       |2
4|    ___|
|   | 3
|___|2
3
```
Will have a resistance of 2.25 ohms (3/4 square plus 3/2 square) if you connect the leads at the east and west sides, and a resistance of 1 ohm (1/3 square plus 2/3 square) if you connect the leads at the north and south sides.

Show that the shape will have infinite resistance if you connect the (perfectly small) leads at the southwest and northeast corners.