Gary in the Rockies and Square-Triangles Gary in the Rockies NW of Boulder, Colorado This picture was taken in 1971 by Carl E. Langenhop, my thesis advisor. In Nebraska we build triangular-shaped pastures as well as square ones, but the triangular ones must have the same area as some square pasture. The Nebraskan countryside is thus a crazy quilt of nearly every triangular shape and size.
None can be right-triangles or isosceles, but all shapes can be arbitrarily approximated.
In pioneer days, to determine each such square-triangle, wooden computers were used which contained three long rolls of paper tape on which were written long lists of strange numbers. In the real world there are billions of hard problems that can be solved with pure mathematics. This has been the story of just one of them.