Hyperbolic Paraboloid

hp-rotatingThe McGowan Associates logo approximates a two-dimensional projection of a hyperbolic paraboloid: a 3D surface formed by two sets of orthogonal parallel lines which rotate through 90° as they move away from the origin point. It is unlike an ordinary paraboloid (x^2+y^2-z=0), which is formed by the rotation of a parabola and resembles a bowl, with infinite extent in two of the three coordinate directions. All unbounded cross-sections of the paraboloid are parabolas. In contrast, changing the sign of the y^2 term produces the hyperbolic paraboloid (x^2-y^2-z=0) which has unbounded hyperbolic cross-sections that extend to infinity in all three coordinate directions. The hyperbolic paraboloid function finds application in the construction of saddle-style roofs, which have been described as “exceptionally stiff” despite a thin cross section, as a consequence of the doubly curved shape which is “literally braced in two directions.” More commonly, the hyperbolic paraboloid is experienced and enjoyed by many in the form of a very popular, highly-consistent potato chip.