paraboloidische

Paraboloidische is an adjective used to describe things relating to or having the shape of a paraboloid. In geometry, a paraboloid is a quadric surface generated by a parabola rotated around its axis (an elliptic paraboloid) or by more general quadratic forms that produce saddle-like surfaces (hyperbolic paraboloids). The term is the German form of the English “paraboloidal” or “paraboloid.”

There are two principal families. The elliptic paraboloid is a smooth, bowl-shaped surface, often described by equations such as z = x^2/a^2 + y^2/b^2 in Cartesian coordinates. It has positive Gaussian curvature and a single focus line, yielding practical optical properties: rays parallel to the axis reflect toward the focus, a principle used in parabolic reflectors and some telescopes.

The hyperbolic paraboloid is saddle-shaped and has negative Gaussian curvature, given by equations like z = x^2/a^2 − y^2/b^2. Its geometry is leveraged in architecture and structural engineering for strength and stability, as seen in curved roofs and shell structures.

Applications across fields include reflectors for satellites and dish antennas, illumination devices, and architectural forms. In mathematics, paraboloidal surfaces are studied for their curvature, focal properties, and role as examples of quadric surfaces. Paraboloidische thus references the broader family of paraboloidal shapes and their geometric and practical implications. See also paraboloid, quadric surface, and hyperbolic paraboloid for related concepts.