Similarities between Hilbert's axioms and Non-Euclidean geometry
Hilbert's axioms and Non-Euclidean geometry have 10 things in common (in Unionpedia): Angle, Axiom, David Hilbert, Euclidean geometry, Euclidean space, Hilbert's axioms, Plane (mathematics), Playfair's axiom, Point (geometry), Primitive notion.
Angle
In Euclidean 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 Hilbert's axioms · Angle and Non-Euclidean geometry ·
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
Axiom and Hilbert's axioms · Axiom and Non-Euclidean geometry ·
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.
David Hilbert and Hilbert's axioms · David Hilbert and Non-Euclidean geometry ·
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements.
Euclidean geometry and Hilbert's axioms · Euclidean geometry and Non-Euclidean geometry ·
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space.
Euclidean space and Hilbert's axioms · Euclidean space and Non-Euclidean geometry ·
Hilbert's axioms
Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry.
Hilbert's axioms and Hilbert's axioms · Hilbert's axioms and Non-Euclidean geometry ·
Plane (mathematics)
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely.
Hilbert's axioms and Plane (mathematics) · Non-Euclidean geometry and Plane (mathematics) ·
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. It is equivalent to Euclid's parallel postulate in the context of Euclidean geometry and was named after the Scottish mathematician John Playfair.
Hilbert's axioms and Playfair's axiom · Non-Euclidean geometry and Playfair's axiom ·
Point (geometry)
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces.
Hilbert's axioms and Point (geometry) · Non-Euclidean geometry and Point (geometry) ·
Primitive notion
In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts.
Hilbert's axioms and Primitive notion · Non-Euclidean geometry and Primitive notion ·
The list above answers the following questions
- What Hilbert's axioms and Non-Euclidean geometry have in common
- What are the similarities between Hilbert's axioms and Non-Euclidean geometry
Hilbert's axioms and Non-Euclidean geometry Comparison
Hilbert's axioms has 36 relations, while Non-Euclidean geometry has 172. As they have in common 10, the Jaccard index is 4.81% = 10 / (36 + 172).
References
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