Fold the Graph of a Cubic Equation

With repeated folds, you can reproduce the graph of a cubic equation.

Steps

1. Draw a point A on a piece of paper in about the middle of the page.
   
2. Poke a small hole at a second point B with your pencil about 4 cm. up from the bottom edge (with the paper in landscape orientation) and a little to the right of point A. The placement of these points doesn't have to be exact. If you place them in different locations, you will still get the graph of a cubic, but the curves will look different than what is shown.
   
3. Fold the paper so a point on the bottom edge of the page touches point A.
   
4. Mark the spot on the paper through the hole at point B. You might need to turn the paper over to make the mark. Unfold.
   
5. Line up a different location on the bottom edge with point A. Mark where B is and unfold.
   
6. Repeat many times until you can see a curve. This curve is the graph of a cubic equation in the form .
   

Links

• For a great description of the math behind this folding and many other interesting projects linking math and origami buy Thomas Hull's book
• Also visit his web site for links to other origami-related projects including a fold-it-yourself CD/DVD case.

References

• (Hull 2006)