Fold a Golden Rectangle

Construct a golden rectangle by folding. A golden rectangle is one with a ratio of length to width of the golden mean, about 1.618. This ratio pops up in many diverse situations: from the ratio of successive terms in the Fibonacci series to the ratio of a diagonal to a side length of a pentagon.

Steps

1. Cut your paper in half lengthwise Neither an A4-sized nor an 8.5 x 11 inch piece of paper is long enough to make a golden rectangle if you use its whole width.
   
2. Fold a square in the end of the paper. Open.
   
3. Fold the square in half and open again.
   
4. Fold the bottom of the paper up so that the bottom edge of the paper goes through the top right-hand corner of the square. Use the intersection of the halfway line and the bottom edge as a pivot.
   
5. Mark the point where the bottom edge meets the top corner of the square by folding the paper down at that point. Open the paper again and fold again at the most recent crease to extend the crease to the top of the paper
   
6. Fold along same crease again. Open.
   
7. The final crease marks the length of the golden rectangle.
   

Notes

• You don't need to cut your paper in half as suggested in the first step. You should cut enough off, though, to ensure that the length of your paper is greater than 1.618 times the width.
  
• If you cut the square off of your golden rectangle, you are left with another, smaller golden rectangle. You can continue to cut off squares off golden rectangles and be left with another.