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A straight line in hyperbolic n-space is modeled by a geodesic on the hyperboloid. A geodesic on the hyperboloid is the (non-empty) intersection of the hyperboloid with a two-dimensional linear subspace (including the origin) of the n+1-dimensional Minkowski space. If we take u and v to be basis vectors of that linear subspace with
A cross-section of a solid right circular cylinder extending between two bases is a disk if the cross-section is parallel to the cylinder's base, or an elliptic region (see diagram at right) if it is neither parallel nor perpendicular to the base. If the cutting plane is perpendicular to the base it consists of a rectangle (not shown) unless it ...
In a plane, given an axis (line) and a point not on that axis, there is only one hypercycle through that point with the given axis (compare with Playfair's axiom for Euclidean geometry). No three points of a hypercycle are on a circle. A hypercycle is symmetrical to each line perpendicular to it.
D 1h and C 2v: group of order 4 with a reflection in a plane and a 180° rotation through a line in that plane; D 1d and C 2h: group of order 4 with a reflection in a plane and a 180° rotation through a line perpendicular to that plane. S 2 is the group of order 2 with a single inversion (C i). "Equal" is meant here as the same up to conjugacy ...
D 1h and C 2v: group of order 4 with a reflection in a plane and a 180° rotation about a line in that plane. D 1d and C 2h: group of order 4 with a reflection in a plane and a 180° rotation about a line perpendicular to that plane. For n = 2 there is not one main axis and two additional axes, but there are three equivalent ones.
Jay-Z made rare comments about his wife Beyoncé and their three children after being accused in a civil lawsuit of raping a 13-year-old girl along with Sean "Diddy" Combs in 2000.. On Sunday, Dec ...
If | | | | >, the line has direction d; the plane that includes the origin and the line L has normal vector m; the line is tangent to a circle on that plane (normal to m and perpendicular to the plane of the picture) centered at the origin and with radius | | | |. Example.
Richie invited Hilton over to watch parts of the show since she hadn’t seen a full episode since it debuted. “It was very funny,” Richie says; however, she admits she found one aspect of it ...