I found this interesting problem from a friend (From Arthur Engel's-Problem Solving Strategies book).
The method to begin the problem is as follows-
Step 1.Take a rectangular strip of paper
Step 2.We all know how to make a knot.Do the same (make a knot) using the strip of paper and fold it along the creases to form a polygon.
(If you are having a problem to make the knot please go to this link to see how to do it. See here )
Step 3.Prove that the polygon $abcde$ formed is regular.
What I could make out from the thing-
When I open the fold again I get this-
Note:-e is mentioned by dotted lines with pencil since e lies in the opposite side of the paper.
Now,my intuition somehow suggest that $a$ and $b$ must be mutually parallel and $d$ and $e$ must also be parallel.(Since then they would become congruent trapeziums).
But unfortunately I have no clue on how to prove this or how to prove that they are equal to $c$.
Any help or response is highly appreciated and thanks a lot in advance!!