Hyperbolic Paraboloid

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.