in a rectangular grid 3600x288 (or any large rectangle with an even number of units) how can I determine the number of vertices a diagonal line will pass through?

Here's a hint, Matthew.

When you reduce the fraction to lowest terms, what factor are you reducing by?
288 / 3600 = (2 / 25) x (144 / 144)
So the diagonal passes through 144 + 1 = 145 vertices, including the actual corners.

Stephen and Penny

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