Golden Ratio by Paper Folding
Given a square piece of paper with edge , make a crease so that . Make another crease so that . Then . Thus , which is the golden ratio.[more]
It is not easy to make the creases. The circle with center at and radius should pass through and should be its tangent.[less]
 T. S. Row, Geometric Exercises In Paper Folding (W. W. Beman and D. E. Smith, eds.), New York: Dover Publications, 1966 pp. 19–20.