In geometry, the hyperboloid model, also known as the Minkowski model or the Lorentz model (after Hermann Minkowski and Hendrik Lorentz), is a model of n-dimensional hyperbolic geometry in which points are represented by the points on the forward sheet S+ of a two-sheeted hyperboloid in (n+1)-dimensional Minkowski space and m-planes are represented by the intersections of the (m+1)-planes in Minkowski space with S+. The hyperbolic distance function admits a simple expression in this model. The hyperboloid model of the n-dimensional hyperbolic space is closely related to the Beltrami–Klein model and to the Poincaré disk model as they are projective models in the sense that the isometry group is a subgroup of the projective group.
Read more about Hyperboloid Model: Minkowski Quadratic Form, Isometries, History
Famous quotes containing the word model:
“I had a wonderful job. I worked for a big model agency in Manhattan.... When I got on the subway to go to work, it was like traveling into another world. Oh, the shops were beautiful, we had Bergdorf’s, Bendel’s, Bonwit’s, DePinna. The women wore hats and gloves. Another world. At home, it was cooking, cleaning, taking care of the kids, going to PTA, Girl Scouts. But when I got into the office, everything was different, I was different.”
—Estelle Shuster (b. c. 1923)