Faster access than browser!Similarities between Euclidean geometry and Hyperbolic geometry
Euclidean geometry and Hyperbolic geometry have 21 things in common (in Unionpedia): Angle, Axiom, Cartesian coordinate system, Coordinate system, Curvature, Elliptic geometry, Euclid, Euclid's Elements, Geometric transformation, Geometry, János Bolyai, Metric space, Nikolai Lobachevsky, Non-Euclidean geometry, Parallel postulate, Plane (geometry), Playfair's axiom, Proclus, Projective geometry, Proof by contradiction, Radian.
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.
Angle and Euclidean geometry · Angle and Hyperbolic geometry ·
Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Axiom and Euclidean geometry · Axiom and Hyperbolic geometry ·
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
Cartesian coordinate system and Euclidean geometry · Cartesian coordinate system and Hyperbolic geometry ·
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Coordinate system and Euclidean geometry · Coordinate system and Hyperbolic geometry ·
Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
Curvature and Euclidean geometry · Curvature and Hyperbolic geometry ·
Elliptic geometry
Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.
Elliptic geometry and Euclidean geometry · Elliptic geometry and Hyperbolic geometry ·
Euclid
Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".
Euclid and Euclidean geometry · Euclid and Hyperbolic geometry ·
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.
Euclid's Elements and Euclidean geometry · Euclid's Elements and Hyperbolic geometry ·
Geometric transformation
A geometric transformation is any bijection of a set having some geometric structure to itself or another such set.
Euclidean geometry and Geometric transformation · Geometric transformation and Hyperbolic geometry ·
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.
Euclidean geometry and Geometry · Geometry and Hyperbolic geometry ·
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.
Euclidean geometry and János Bolyai · Hyperbolic geometry and János Bolyai ·
Metric space
In mathematics, a metric space is a set for which distances between all members of the set are defined.
Euclidean geometry and Metric space · Hyperbolic geometry and Metric space ·
Nikolai Lobachevsky
Nikolai Ivanovich Lobachevsky (a; –) was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry and also his fundamental study on Dirichlet integrals known as Lobachevsky integral formula.
Euclidean geometry and Nikolai Lobachevsky · Hyperbolic geometry and Nikolai Lobachevsky ·
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
Euclidean geometry and Non-Euclidean geometry · Hyperbolic geometry and Non-Euclidean geometry ·
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.
Euclidean geometry and Parallel postulate · Hyperbolic geometry and Parallel postulate ·
Plane (geometry)
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
Euclidean geometry and Plane (geometry) · Hyperbolic geometry and Plane (geometry) ·
Playfair's axiom
In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid (the parallel postulate): In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
Euclidean geometry and Playfair's axiom · Hyperbolic geometry and Playfair's axiom ·
Proclus
Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).
Euclidean geometry and Proclus · Hyperbolic geometry and Proclus ·
Projective geometry
Projective geometry is a topic in mathematics.
Euclidean geometry and Projective geometry · Hyperbolic geometry and Projective geometry ·
Proof by contradiction
In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.
Euclidean geometry and Proof by contradiction · Hyperbolic geometry and Proof by contradiction ·
Radian
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
Euclidean geometry and Radian · Hyperbolic geometry and Radian ·
The list above answers the following questions
- What Euclidean geometry and Hyperbolic geometry have in common
- What are the similarities between Euclidean geometry and Hyperbolic geometry
Euclidean geometry and Hyperbolic geometry Comparison
Euclidean geometry has 153 relations, while Hyperbolic geometry has 175. As they have in common 21, the Jaccard index is 6.40% = 21 / (153 + 175).
References
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