Start with a unit square (a rectangle with both sides equal to 1, call it R1). Attach a rectangle of area 1 to its right side, then attach a rectangle of area 1 to its top. The border of this new shape is another rectangle, call it R2. We can repeat the process with R2 to create a new rectangle R3, and then repeat again, and so on. What is the ratio of the length to the width of Rn, as n goes to infinity? The answer is surprising!
My blog post for this puzzle
Proof of final formula (this spoils the answer, so watch the video first)
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Brian M. Mooney
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