Hyperbole 03 Pendant

There's a shape that metalsmiths make when learning anticlastic raising called a hyperbolic paraboloid, because that's the mathematical surface it resembles, a square with one pair of corners raised and the other pair lowered.  If you're ambitious, however, you can continue curving the corners until they meet.  The resulting shape is pretty, but it's no longer a hyperbolic paraboloid.  We haven't yet found a common mathematical name for that shape, but we came up with an equation that has that shape.  It's a surface with negative Gaussian curvature, but it's not a hyperbolic paraboloid and it's not a hyperboloid, so for now we're calling it a hyperbole.  Let's call it a pun.  

Hyperbole 03 has a ripple added along the v direction.  Hyperbole 03 Pendant is suitable for printing in precious metals.  

The toolkit we use to turn these equations into printable objects is called Anethole, and is available on GitHub. The hyperbole starts with a function that gives the edges of a square in polar coordinates, then rolls it up as a half pipe, then applies a ruffle function (the same one used in the Equation To Object tutorial) with a period of pi.  The images for this product include the equation which produces Hyperbole 03.