Start with a square piece of paper. Label the vertices ABCD. Pick a point on CD and label it E. Fold along the line BE. Label the new location of C as C'. Find the point F on AD such that when folding along BF it makes the new location of A coincide with C'. Now lastly find a point G on AD such that when folding along EG it makes the new location of D lie on EF (either EC' or A'F). After all 3 of these folds are completed you should have a new irregularly shaped quadrilateral FBEG.
For simplicity's sake assume the original square
is of unit length. Now the 2 problems are:
1) If x is the length of CE, then give an equation
for the area of FBEG based on x.
2) Find the x that maximizes the area of FBEG
1) The required area of FBEG in terms of x is:
1 + x^3 x^4
= --------------- -- ----------
2 1 + x
2) The required value of x is approximately .7207593 to give an area of .53038081089284.
** Will try my best to posit an independent analytical explanation of my own.
Edited on January 18, 2024, 9:50 pm
Puzzle Answer
