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September 22, 2014

September 22, 2014

Posted by **Kelsey** on Saturday, October 29, 2011 at 5:41pm.

- math (calculus) -
**Steve**, Monday, October 31, 2011 at 12:14amIf we label the lower left corner A, and go clockwise for B,C,D

then with some actual folding experimentation, we see that P can go along side BC at a distance x from B, which can vary from b-sqrt(b^2-a^2) to a. Anywhere else the fold produces a flap that extends beyond the sheet.

When x = b-sqrt(b^2-a^2) the fold length is just the long side of the rectangle, b. That is, P is a distance sqrt(b^2-a^2) from C.

When x = a, the fold length is just the diagonal of a square, a√2

It's late. I'll let you figure out in which cases one is greater than the other.

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