Optimize the Length of the Crease of a Folded Piece of Paper

distance x

2

A sheet of legal paper is 8.5 by 11.75 inches long. The lower-left corner is brought to a point

x

inches from the upper-left corner and folded to form a crease. This Demonstration shows a graph of the crease length as a function of

x

and a diagram of the folded paper. By moving the slider, you can estimate the length of the shortest and longest possible crease. The exact shortest possible crease (

51

3

8

≈11.04

) and the exact longest possible crease (

47

68

47

2

(47-9

13

)

≈12.78

) may be determined by using Mathematica or traditional calculus techniques.