Given a square piece of paper ABCD.
Using paper folding alone, construct a line segment having the length equal to one-sixth of AB.
1. Fold so AB goes onto CD. Let the endpoints of the fold be E and F, with E on AD and F on BC. E and F are the midpoints of AD and BC.
2. Fold along the lines BD and AF. Call their point of intersection G. Point G will be 1/3 of the way in from side AB and BC.
3. Fold parallel to AD/BC so that the fold includes G. Let H be the intersection of this fold and EF. GH is then 1/6 AB.