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(mathematics) Of or pertaining to a broad field of mathematics that originates from the problem of … (where r is on the sphere) represents the great circle in the plane perpendicular to r. Opposite points r and –r correspond to oppositely directed circles. r Definition 2 is wrong. With O the center of the hemisphere, a point P in σ determines a line OP intersecting the hemisphere, and any line L ⊂ σ determines a plane OL which intersects the hemisphere in half of a great circle. Working in s… The case v = 1 corresponds to left Clifford translation. , ( cal adj. In the case that u and v are quaternion conjugates of one another, the motion is a spatial rotation, and their vector part is the axis of rotation. ⋅ z Elliptic geometry definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Elliptic geometry is also like Euclidean geometry in that space is continuous, homogeneous, isotropic, and without boundaries. Philosophical Transactions of the Royal Society of London, On quaternions or a new system of imaginaries in algebra, "On isotropic congruences of lines in elliptic three-space", "Foundations and goals of analytical kinematics", https://en.wikipedia.org/w/index.php?title=Elliptic_geometry&oldid=982027372, Creative Commons Attribution-ShareAlike License, This page was last edited on 5 October 2020, at 19:43. In this context, an elliptic curve is a plane curve defined by an equation of the form = + + where a and b are real numbers. Definition of Elliptic geometry. Finite Geometry. Meaning of elliptic. Please tell us where you read or heard it (including the quote, if possible). Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no lines parallel to a given line." Look it up now! (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle. It is said that the modulus or norm of z is one (Hamilton called it the tensor of z). One way in which elliptic geometry differs from Euclidean geometry is that the sum of the interior angles of a triangle is greater than 180 degrees. Elliptic geometry is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p.Elliptic geometry, like hyperbolic geometry, violates Euclid's parallel postulate, which can be interpreted as asserting that there is exactly one line parallel to L passing through p.In elliptic geometry, there are no parallel lines at all. Elliptic or Riemannian geometry synonyms, Elliptic or Riemannian geometry pronunciation, Elliptic or Riemannian geometry translation, English dictionary definition of Elliptic or Riemannian geometry. Euclidean geometry:Playfair's version: "Given a line l and a point P not on l, there exists a unique line m through P that is parallel to l." Euclid's version: "Suppose that a line l meets two other lines m and n so that the sum of the interior angles on one side of l is less than 180°. A model representing the same space as the hyperspherical model can be obtained by means of stereographic projection. The reason for doing this is that it allows elliptic geometry to satisfy the axiom that there is a unique line passing through any two points. Definition 6.2.1. Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no lines parallel to a given line." Define elliptic geometry by Webster's Dictionary, WordNet Lexical Database, Dictionary of Computing, Legal Dictionary, Medical Dictionary, Dream Dictionary. For example, the first and fourth of Euclid's postulates, that there is a unique line between any two points and that all right angles are equal, hold in elliptic geometry. z Elliptic Geometry Riemannian Geometry A non-Euclidean geometry in which there are no parallel lines.This geometry is usually thought of as taking place on the surface of a sphere. This is because there are no antipodal points in elliptic geometry. Rather than derive the arc-length formula here as we did for hyperbolic geometry, we state the following definition and note the single sign difference from the hyperbolic case. In elliptic space, arc length is less than π, so arcs may be parametrized with θ in [0, π) or (–π/2, π/2].[5]. exp Definition •A Lune is defined by the intersection of two great circles and is determined by the angles formed at the antipodal points located at the intersection of the two great circles, which form the vertices of the two angles. Elliptic geometry is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. Elliptic geometry, like hyperbolic geometry, violates Euclid's parallel postulate, which can be interpreted as asserting that there is exactly one line parallel to L passing through p. In elliptic geometry, there are no parallel lines at all. Elliptic geometry definition is - geometry that adopts all of Euclid's axioms except the parallel axiom which is replaced by the axiom that through a point in a plane there pass no lines that do not intersect a given line in the plane. = Lines in this model are great circles, i.e., intersections of the hypersphere with flat hypersurfaces of dimension n passing through the origin. "Bernhard Riemann pioneered elliptic geometry" Exact synonyms: Riemannian Geometry Category relationships: Math, Mathematics, Maths Elliptic geometry is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. Elliptic geometry, like hyperbolic geometry, violates Euclid's parallel postulate, which can be interpreted as asserting that there is exactly one line parallel to L passing through p.In elliptic geometry, there are no parallel lines at all. For example, this is achieved in the hyperspherical model (described below) by making the "points" in our geometry actually be pairs of opposite points on a sphere. Elliptic geometry was apparently first discussed by B. Riemann in his lecture “Über die Hypothesen, welche der Geometrie zu Grunde liegen” (On the Hypo