Why Does Tying a Knot on a Rectangular Piece of Paper Form a Perfect Pentagon?

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Tying a knot in a rectangular piece of paper results in a perfect pentagon due to the geometric properties of the knot's structure. The knot's tension and the way it interacts with the paper create specific angles and lengths that align to form a pentagon. Resources like "Cut the Knot" and Jim Loy's geometry site provide insights into this phenomenon. The discussion emphasizes the mathematical and geometric principles behind this intriguing observation. Understanding these concepts can deepen appreciation for the relationship between geometry and everyday objects.
Icebreaker
Take a long rectangular piece of paper, and tie a simple knot. Carefully pull it into place and the location of the knot will be a perfect pentagon. Why?

(Not a brain teaser, I really don't know the answer.)
 
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No, in fact, I did not.
 

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