Fold Three Pentagons from a Strip of Paper

You can create three pentagons of different sizes from one, long strip of paper without measuring any angles or using any templates to make your creases. As you repeatedly make a sequence of folds, any error in the angle you started with will diminish.

Materials

• A long strip of paper. You can use any width, but the paper will have to be about 16 to 20 times as long as it is wide. You can use adding machine paper from a roll or cut strips of wrapping paper or newspaper and tape them together.
  

Steps

1. Make one crease near the end of your paper that is about 36° from the top edge of your paper. The measurement does not have to be exact. As a matter of fact, after a few cycles through steps 2 - 5, most of the error you make in this angle will be automatically corrected.
   
2. Fold the top edge so it lies along this crease. Make a crease and open the paper.
   
3. Fold the top edge a second time along the most recent crease. Open.
   
4. Switch to the bottom edge. Fold it up along the latest crease. Open.
   
5. Fold the bottom edge a second time along the latest crease. Open.
   
6. Continue by repeating steps 2 - 5 alternating two folds from the top edge and two folds from the bottom edge. With each iteration, your angles will get closer to their appropriate values. So even if your first fold was inaccurate, subsequent folds will be better. You can simply tear off a few of the first sets of triangles and work with the more accurate ones to build your models.
   
7. Fold the strip of paper at every short crease to make a small pentagon.
   
8. Fold the strip of paper at every long crease to make a larger pentagon.
   
9. Fold the strip of paper first at a long crease, then at a short one to make the largest pentagon.
   

References

• (Hilton, Holton and Pedersen 1997), (Hilton, Holton and Pedersen 2002)