Geographic Graph Theory

by agbdmrbirdyface, Aug 10, 2016, 7:15 PM

This is a simple graph theory problem... with a geo problem thrown in for good measure.
Classic Problem wrote:
Suppose you are to tile the Earth with square tiles, with the following rules:

Touching tiles must match along their edges, and they should have roughly square corners. Hence, if two tiles touch, they must touch at a corner or along an entire edge of each tile. Wherever tiles meet at a corner, exactly 4 tiles must meet at that corner. The tiles don't have to be exactly square, and can be of different sizes, but each tile should have side length at least an inch and at most one mile.

Show it is either possible or impossible to find such a tiling. If it is impossible, show why it is, and if it is possible, find such a configuration.

Solution:

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Sidenote: Since Euler's Formula turns out to be zero, this tiling is actually possible on a torus! All we need to do now to tile Earth IRL is to simply figure out a way to drill all the way through Earth.

by agbdmrbirdyface, Aug 11, 2016, 3:45 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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