Given A=(a,0), B=(0,0), and C=(0,a)
Let f(a)=the total number of unit equilateral triangles XYZ that can be formed such that the lengths AX, BY, and CZ are all 1 unit.

Give a piecewise definition by intervals for f(a)

(In reply to re: initial constraints (a start) by Charlie)

yeah I had it a feeling it was not the lowest upper bound you can place on a, but I figured it was a start.  Also in my second post I made some miscalcuations but I am currently running a program in Mathematica that is finding all points at which f(a) changes value.  I'm only doing it to 2 digits of accuracy for right now so I can at least see where about these points are, later I plan on letting the code run for much longer to allow for more precission.

Posted by Daniel on 2009-09-14 22:26:20