Elliptic lines through versor u may be of the form, They are the right and left Clifford translations of u along an elliptic line through 1. Pronunciation of elliptic geometry and its etymology. When doing trigonometry on Earth or the celestial sphere, the sides of the triangles are great circle arcs. Therefore any result in Euclidean geometry that follows from these three postulates will hold in elliptic geometry, such as proposition 1 from book I of the Elements, which states that given any line segment, an equilateral triangle can be constructed with the segment as its base.   Relativity theory implies that the universe is Euclidean, hyperbolic, or elliptic depending on whether the universe contains an equal, more, or less amount of matter and energy than a certain fixed amount. [9]) It therefore follows that elementary elliptic geometry is also self-consistent and complete. r Noun. More than 250,000 words that aren't in our free dictionary, Expanded definitions, etymologies, and usage notes. The hemisphere is bounded by a plane through O and parallel to σ. Example sentences containing elliptic geometry 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. Elliptic geometry definition at Dictionary.com, a free online dictionary with pronunciation, synonyms and translation. Hyperbolic geometry is like dealing with the surface of a donut and elliptic geometry is like dealing with the surface of a donut hole. Because spherical elliptic geometry can be modeled as, for example, a spherical subspace of a Euclidean space, it follows that if Euclidean geometry is self-consistent, so is spherical elliptic geometry. Definition of elliptic in the Definitions.net dictionary. Hyperbolic geometry is also known as saddle geometry or Lobachevskian geometry. cos For Notice for example that it is similar in form to the function sin ⁡ − 1 (x) \sin^{-1}(x) sin − 1 (x) which is given by the integral from 0 to x … Related words - elliptic geometry synonyms, antonyms, hypernyms and hyponyms. θ The hemisphere is bounded by a plane through O and parallel to σ. z The "lines" are great circles, and the "points" are pairs of diametrically opposed points.As a result, all "lines" intersect. One uses directed arcs on great circles of the sphere. Access to elliptic space structure is provided through the vector algebra of William Rowan Hamilton: he envisioned a sphere as a domain of square roots of minus one. + In spherical geometry any two great circles always intersect at exactly two points. 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. ⋅ a In Euclidean geometry, a figure can be scaled up or scaled down indefinitely, and the resulting figures are similar, i.e., they have the same angles and the same internal proportions. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non-orientable. In general, area and volume do not scale as the second and third powers of linear dimensions. Elliptic geometry is a geometry in which no parallel lines exist. Elliptic geometry has a variety of properties that differ from those of classical Euclidean plane geometry. The Pythagorean result is recovered in the limit of small triangles. 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