Three pentagram-shaped stars (the stars formed from the diagonals of a regular pentagon) are stacked up so that the bottom two ends of the tips touch the middle ends of the tips of the star below. (See diagram.)

The distance from the top of the stack to the floor (where the bottom star's "feet" rest) is 4 feet.

What is the distance between the bottom two ends of the tips of the stack that touch the floor?

I used a trig solution and have confirmed the final answer obtained by:
nikki
brianjn
vectorboy, and
CeeAnne

I also did calculations to verify that the top of the next smallest pentagram fits exactly into the "inside corner" of the larger pentagram above.

In fact an exact solution for the answer is:

4 / {cos(18) * (PHI^3 + PHI + 1)}

Edited on July 5, 2005, 8:19 pm

Posted by Larry on 2005-07-05 20:15:02