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
more precision by Daniel)
I'm fairly sure that my recreation of this in GSP shows there's no solution for a=1.960 and above.
Also, for a=1.95644, GSP does confirm the area of 3 solutions does exist, including this point, and also, at 0.73486 having 11 solutions.

Posted by Charlie
on 20090914 23:43:16 