In the Eternal Forest, the trees are perfectly circular, each having a diameter of exactly one meter. They are arranged in a flat, infinite rectangular grid. The center of each tree is ten meters away from the centers of each of its closest neighbors.

There are many paths through the Eternal Forest. Each path is infinite in length, constant in width, and perfectly straight. Trees don't grow on the paths, but every path will have tree trunks touching it on either side.

What is the narrowest possible path through the Eternal Forest?

(In reply to Thoughts by Bob)

I didn't claim the slope 1/9 path was the minimum, only the minimum for slopes of the form 1/n.

I still intend to investigate slopes like 2/3 and 3/4 hopefully to come up with a general formula for the width of the path with slope m/n where m<n and m and n are relatively prime.

My guess is that there will be a narrower path than the one I found (.10432)

Posted by Jer on 2005-05-27 12:06:41