Hyperbole Chain Pendant

Our Hyperbole Chain Pendant is a member of the Mathematical Menagerie, a family of jewelry and sculpture created by writing equations and turning them into 3D printable objects using Anethole.  

There's a shape that metalsmiths make when learning a technique called anticlastic raising. The shape is called an extended 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 mathematically 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.  

The Menagerie includes several variations on the hyperbole equation.  Hyperbole Chain includes four of our hyperbole designs in an interlocked chain.  Hyperbole Chain Pendant is suitable for printing in interlocking precious metals.  Neck chain is not included.  

The toolkit we use to turn these equations into printable objects, Anethole, 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 Anethole's Equation To Object tutorial) with a period of pi.  The images for this product include the equations which produce the hyperbole designs.