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)

the way I'm approaching this is I set up a function in Mathematica that counts the number of triangles possible given a using the FindInstance function.  I am then looking for the transition points p where F(x)<F(p) when x<p.  So far I have found found that on the interval [0,0.5) F(a)=0
on [0.5,051763) F(a)=4
I am still working on 5 digit percision for the remaining transition points (it is taking quite some time to compute as you can imagine).

Edited on September 14, 2009, 7:34 pm

Posted by Daniel on 2009-09-14 19:32:55