74 relations: Albert Einstein, Annals of Mathematics, Brane, Circle group, Coordinate system, Coxeter element, Cross-polytope, Cube, Dimension, Edward Witten, Electromagnetism, Equilateral triangle, Euclidean space, Expansion (geometry), Fundamental interaction, Gauge theory, General relativity, Gerard 't Hooft, Germany, Graviton, Gravity, Hermann Weyl, Hilbert space, Holographic principle, Hypercube, Hypersphere, John Horton Conway, Kaluza–Klein theory, Kissing number problem, Large Hadron Collider, M-theory, Massless particle, Mathematics, Metric tensor, Minkowski space, Oskar Klein, Peter Bergmann, Physics, Real number, Rectified 5-orthoplexes, Regular polytope, Riemann curvature tensor, Scalar (physics), Simplex, Space, Space (mathematics), Spacetime, Square, Stericated 5-simplexes, String theory, ..., Strong interaction, Supergravity, Sweden, Symmetry (physics), Tesseract, Tetrahedron, Theodor Kaluza, Theory of relativity, Time, Triangle, Tuple, Unified field theory, Universe, Valentine Bargmann, Weak interaction, 16-cell, 5-cell, 5-cube, 5-demicube, 5-demicubic honeycomb, 5-manifold, 5-orthoplex, 5-simplex, 5-simplex honeycomb. Expand index (24 more) »

## Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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## Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

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## Brane

In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.

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## Circle group

In mathematics, the circle group, denoted by T, is the multiplicative group of all complex numbers with absolute value 1, that is, the unit circle in the complex plane or simply the unit complex numbers The circle group forms a subgroup of C×, the multiplicative group of all nonzero complex numbers.

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## 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.

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## Coxeter element

In mathematics, the Coxeter number h is the order of a Coxeter element of an irreducible Coxeter group.

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## Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Dimension

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.

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## Edward Witten

Edward Witten (born August 26, 1951) is an American theoretical physicist and professor of mathematical physics at the Institute for Advanced Study in Princeton, New Jersey.

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## Electromagnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

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## Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

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## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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## Expansion (geometry)

In geometry, expansion is a polytope operation where facets are separated and moved radially apart, and new facets are formed at separated elements (vertices, edges, etc.). Equivalently this operation can be imagined by keeping facets in the same position but reducing their size.

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## Fundamental interaction

In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions.

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## Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations.

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## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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## Gerard 't Hooft

Gerardus (Gerard) 't Hooft (born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands.

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## Germany

Germany (Deutschland), officially the Federal Republic of Germany (Bundesrepublik Deutschland), is a sovereign state in central-western Europe.

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## Graviton

In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravity.

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## Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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## Hermann Weyl

Hermann Klaus Hugo Weyl, (9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher.

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## Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.

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## Holographic principle

The holographic principle is a principle of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region—preferably a light-like boundary like a gravitational horizon.

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## Hypercube

In geometry, a hypercube is an ''n''-dimensional analogue of a square and a cube.

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## Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

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## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

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## Kaluza–Klein theory

In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual four of space and time and considered an important precursor to string theory.

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## Kissing number problem

In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.

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## Large Hadron Collider

The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider, the most complex experimental facility ever built and the largest single machine in the world.

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## M-theory

M-theory is a theory in physics that unifies all consistent versions of superstring theory.

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## Massless particle

In particle physics, a massless particle is an elementary particle whose invariant mass is zero.

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## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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## Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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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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## Oskar Klein

Oskar Benjamin Klein (15 September 1894 – 5 February 1977) was a Swedish theoretical physicist.

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## Peter Bergmann

Peter Gabriel Bergmann (Berlin, 24 March 1915 – Seattle, 19 October 2002) was a German-American physicist of Jewish origins best known for his work with Albert Einstein on a unified field theory encompassing all physical interactions.

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## Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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## Rectified 5-orthoplexes

In five-dimensional geometry, a rectified 5-orthoplex is a convex uniform 5-polytope, being a rectification of the regular 5-orthoplex.

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## Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.

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## Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

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## Scalar (physics)

A scalar or scalar quantity in physics is a physical quantity that can be described by a single element of a number field such as a real number, often accompanied by units of measurement.

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## Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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## Space

Space is the boundless three-dimensional extent in which objects and events have relative position and direction.

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## Space (mathematics)

In mathematics, a space is a set (sometimes called a universe) with some added structure.

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## Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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## Stericated 5-simplexes

In five-dimensional geometry, a stericated 5-simplex is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-simplex.

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## String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.

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## Strong interaction

In particle physics, the strong interaction is the mechanism responsible for the strong nuclear force (also called the strong force or nuclear strong force), and is one of the four known fundamental interactions, with the others being electromagnetism, the weak interaction, and gravitation.

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## Supergravity

In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity where supersymmetry obeys locality; in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model.

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## Sweden

Sweden (Sverige), officially the Kingdom of Sweden (Swedish), is a Scandinavian country in Northern Europe.

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## Symmetry (physics)

In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation.

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## Tesseract

In geometry, the tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square.

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## Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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## Theodor Kaluza

Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal, Silesia, German Empire, today part of Opole in Poland – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza–Klein theory involving field equations in five-dimensional space.

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## Theory of relativity

The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity.

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## Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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## Triangle

A triangle is a polygon with three edges and three vertices.

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## Tuple

In mathematics, a tuple is a finite ordered list (sequence) of elements.

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## Unified field theory

In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields.

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## Universe

The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.

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## Valentine Bargmann

Valentine "Valya" Bargmann (April 6, 1908 – July 20, 1989) was a German-American mathematician and theoretical physicist.

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## Weak interaction

In particle physics, the weak interaction (the weak force or weak nuclear force) is the mechanism of interaction between sub-atomic particles that causes radioactive decay and thus plays an essential role in nuclear fission.

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## 16-cell

In four-dimensional geometry, a 16-cell is a regular convex 4-polytope.

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## 5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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## 5-cube

In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces.

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## 5-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed.

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## 5-demicubic honeycomb

The 5-demicube honeycomb, or demipenteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space.

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## 5-manifold

In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear or smooth structure.

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## 5-orthoplex

In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron cells, 32 5-cell 4-faces.

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## 5-simplex

In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope.

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## 5-simplex honeycomb

In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb).

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## Redirects here:

5-dim, 5-dimensional, 5-dimensional space, 5-space, Fifth dimension (geometry), The universe of five dimensions.

## References

[1] https://en.wikipedia.org/wiki/Five-dimensional_space