Curved Folding

surface created by creasing along parabola

This elegant shape was formed by making two parabolic creases. That's it! The curved folds coax the piece of paper into a 3D shape.

Think about the 3D surfaces that you can make out of paper without folding. You can roll a sheet of paper into a cylinder and a cone, but try as you might, you cannot form a sphere without introducing all sorts of kinks, wrinkles, and puckers. The mathematical name for the types of shapes that you can make from paper are developable surfaces. A plane, cylinder, cone (both elliptical and circular) are examples of developable surfaces. The final developable surface is a tangent developable. To picture this type of surface think of a strip of paper that you put waves or twists into. Regular paper folding and curved folding create shapes built from developable surfaces.


  1. Score the crease line that is marked on the pattern and cut out the square.
  2. Pinch along the crease line.