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.