A hyperboloid of one sheet is the unique quadric surface that can be generated by straight lines — it is a doubly-ruled surface, meaning two distinct families of lines lie entirely on it. Rotating a straight line skewed to an axis traces the surface; the minimum circle (the waist) has radius a where x²/a² + y²/a² − z²/c² = 1. This geometry appears in cooling tower design — the straight-line construction is structurally efficient and can be assembled from straight steel rods. The twist angle controls how steeply the ruling lines lean relative to the axis, directly revealing the hyperbolic throat shape.