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 initial constraints (a start) by Daniel)

In order for a solution to exist wouldn't a have to be at most 3/sqrt(2), as Z needs to be 1 unit from C, X needs to be 1 unit from A and Z needs to be 1 unit from X. If in a line then a needs to be than the length of 3/sqrt(2) as an isosceles rt triangle is formed. If not in a straight line (as will actually be the case), a must be less than this.

Posted by Charlie on 2009-09-14 19:43:49