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Unit lengths from movable points to unit triangles. (Posted on 2009-09-14) Difficulty: 4 of 5
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)

No Solution Yet Submitted by Jer    
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re: more precision | Comment 8 of 11 |
(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 2009-09-14 23:43:16
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