Hyperbolic Paraboloid

thingiverse

The string represents a hyperbolic paraboloid, a type of quadric surface. Generally, hyperbolic paraboloids are defined by the equation z= y^2/a^2-x^2/b^2. At the center of a hyperbolic paraboloid is a saddle point. At this point the surface is both curving upwards in one direction and downwards in another. I designed this object by exploiting an interesting feature of hyperbolic paraboloids – they are doubly ruled. This means that each point has two lines passing through it that also lie on the quadric surface. The curved shape can be defined by a series of straight lines. Using string to represent these straight lines demonstrates the doubly ruled nature of hyperbolic paraboloids. I made this seemingly complex object from very simple rules. Instructions This part was made on an Epilog Mini 18 Laser. It was vector cut out of 3mm acrylic. Both sides need to be made twice, only one base is needed. The parts were glued together with acrylic glue. The opening for the string is 1/10in. This left more than enough room for the string I used, however for thicker string this size may need to increase.