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Absolute geometry and Hyperbolic geometry

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Absolute geometry and Hyperbolic geometry

Absolute geometry vs. Hyperbolic geometry

Absolute geometry is a geometry based on an axiom system for Euclidean geometry with the parallel postulate removed and none of its alternatives used in place of it. In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

Similarities between Absolute geometry and Hyperbolic geometry

Absolute geometry and Hyperbolic geometry have 12 things in common (in Unionpedia): Angle, Elliptic geometry, Euclid's Elements, Euclidean geometry, Geometry, Hyperbolic geometry, János Bolyai, Minkowski space, Non-Euclidean geometry, Parallel postulate, Saccheri quadrilateral, Spherical geometry.

Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Elliptic geometry

Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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János Bolyai

János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Non-Euclidean geometry

In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.

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Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.

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Saccheri quadrilateral

A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base.

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Spherical geometry

Spherical geometry is the geometry of the two-dimensional surface of a sphere.

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The list above answers the following questions

Absolute geometry and Hyperbolic geometry Comparison

Absolute geometry has 31 relations, while Hyperbolic geometry has 175. As they have in common 12, the Jaccard index is 5.83% = 12 / (31 + 175).

References

This article shows the relationship between Absolute geometry and Hyperbolic geometry. To access each article from which the information was extracted, please visit:

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