The Pentagon Problem Stephanie J. Morris The "Pentagon Problem"
begins with any pentagon. A second pentagon, in blue, is formed
by connecting the midpoints of each side of the first pentagon.
A third pentagon, in green, is constructed the same way by
connecting the midpoints of pentagon 2. "As long as each side of
the two smaller pentagons are formed by joining the midpoints of
the next larger pentagon, the two ratios of the areas will
always be equal, and the two ratios of the perimeters will
always be equal, no matter what shape the largest pentagon Do
you think that this conjecture is valid? Why or why not? When I
first read this conjecture, I thought that it seemed pretty
"logical" that the conjecture was a valid one. I believed that
after several constructions of various pentagons and the
comparisons of the above mentioned ratios, that I could come up
with a proof of this conjecture. However, after I began
investigating the conjecture with the Geometer's Sketchpad, I
soon learned that maybe my own assump