In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. When N=5, one of these numbers is sometimes colloquially called the fifth dimension. This usage may occur in casual discussions about the fourth dimension. Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics and particle physics. Fifth Dimension may be a reference to: Fifth dimension, the mathematical or physical, geometry-related, abstraction The Fifth Dimension, a Grammy Award winning popular music vocal group who had a number of hits during the late 1960s and early 1970s Fifth Dimension (album), an album and 5D (Fifth... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... In mathematics, a vector space (or linear space) is a collection of objects (called vectors) that, informally speaking, may be scaled and added. ... For other uses, see Fourth dimension (disambiguation). ... For other uses, see Universe (disambiguation). ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

Fifth dimensions in physics

In physics, the Fifth dimension is a hypothetical extra dimension beyond the usual three spatial and one time dimensions. Some scientists have speculated that the graviton, a particle thought to carry the force of gravity, may "leak" into the fifth or higher dimensions which would explain how gravity is significantly weaker than the other three fundamental forces. The Kaluza-Klein theory used a fifth dimension to unify gravity with the electromagnetic force, and now is seen as essentially a gauge theory with gauge group the circle group. M-theory suggests that space-time has eleven dimensions, seven of which are "rolled up" to below the sub-atomic level. This article is about the idea of space. ... Look up time in Wiktionary, the free dictionary. ... This article is about the hypothetical particle. ... Gravity is a force of attraction that acts between bodies that have mass. ... A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... In physics, Kaluza-Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. ... In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, the circle group, denoted by T (or in blackboard bold by ), is the multiplicative group of all complex numbers with absolute value 1. ... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ...

In 1993 the physicist Gerard 't Hooft put forward the holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimensions. For example, holograms are three dimensional pictures placed on a two dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the spacetime fabric. Gerard t Hooft at Harvard University Gerardus (Gerard) t Hooft (born July 5, 1946) is a professor in theoretical physics at Utrecht University, The Netherlands. ... The holographic principle is a speculative conjecture about quantum gravity theories, proposed by Gerard t Hooft and improved and promoted by Leonard Susskind, claiming that all of the information contained in a volume of space can be represented by a theory which lives in the boundary of that region. ...

It has occasionally been stated the Fifth dimension is probability, meaning that the fifth dimension is the full amount of possibilities that could happen or, in other words, alternate realities. Probability is the likelihood that something is the case or will happen. ... Parallel universe, alternate reality, etc. ...

Five-dimensional geometry

Polytopes

Demonstration of objects with 1 to 5 dimensions

In five or more dimensions, only three regular polytopes exist. For N dimensions, they are: Image File history File links Dice_analogy-_1_to_5_dimensions. ... Image File history File links Dice_analogy-_1_to_5_dimensions. ... A dodecahedron, one of the five Platonic solids. ...

1. The simplex, with N+1 vertices, all at equal distances from one another; it consists of N+1 simplices of dimension N-1. The three-dimensional simplex is the tetrahedron, and the five-dimensional simplex is a hexatetron; it has 6 vertices, 15 edges, 20 faces (each a triangle), 15 cells (or solids - each a tetrahedron), and 6 hypercells (each a pentachoron).
2. The hypercubes, having 2^N vertices whose coordinates may be written (±1,±1, ..., ±1) for some suitable set of axes. It consists of 2N hypercubes of the next lower dimension. The five-dimensional hypercube is a decateron or penteract; it has 32 vertices, 80 edges, 80 faces (each a square), 40 cells (each a cube), and 10 hypercells (each a tesseract).
3. The cross polytope, with 2N vertices, paired on opposite sides of the N coordinate axes; it consists of 2^N simplices of dimension N-1. The five-dimensional cross polytope is a triacontakaiditeron or pentacross, with 10 vertices, 40 edges, 80 faces (each a triangle), 80 cells (each a tetrahedron), and 32 hypercells (each a pentachoron).

The dual of a simplex is a simplex. The hypercube and cross-polytope of the same dimension are dual to each other. A 3-simplex or tetrahedron In geometry, a simplex (plural simplexes or simplices) or n-simplex is an n-dimensional analogue of a triangle. ... A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... A triangle. ... A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... The pentachoron, also called a pentatope or 4-simplex, is the simplest convex regular polychoron (a type of four-dimensional geometric figure). ... A square A projection of a cube (into a two-dimensional image) A projection of a hypercube (into a two-dimensional image) In geometry, a hypercube is an n-dimensional analogue of a square (n = 2) and a cube (n = 3). ... A penteract is a name for a five dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract hypercells. ... For other uses, see Square. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... For other uses, see Tesseract (disambiguation). ... In geometry, a cross-polytope, or orthoplex, is a regular, convex polytope that exists in any number of dimensions. ... A 3-simplex or tetrahedron In geometry, a simplex (plural simplexes or simplices) or n-simplex is an n-dimensional analogue of a triangle. ... (Precisely, the Perspective projection 3D to 2D of) stereographic projection 4D to 3D of Schlegel diagram 5D to 4D of Pentacross. ... A triangle. ... A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... The pentachoron, also called a pentatope or 4-simplex, is the simplest convex regular polychoron (a type of four-dimensional geometric figure). ... In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the others. ...

Here are three projected images of the edges of a regular decateron or penteract: A penteract is a name for a five dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract hypercells. ...

Click any image to see a larger view

See also: 5-polytope, and List of regular 5-polytopes Image File history File links Download high-resolution version (760x607, 60 KB) Made by Oftefs using Solid Edge I, the creator of this work, hereby release it into the public domain. ... Image File history File links Download high-resolution version (760x607, 59 KB) Made by Oftefs using Solid Edge I, the creator of this work, hereby release it into the public domain. ... Image File history File links This is a lossless scalable vector image. ... In geometry, a five-dimensional polytope, or 5-polytope, is a polytope in 5-dimensional space. ... This page lists the regular polytopes in Euclidean space. ...

Hypersphere

The hypervolume of a Hypersphere in 5-space is: 2-sphere wireframe as an orthogonal projection Just as a stereographic projection can project a spheres surface to a plane, it can also project a 3-spheres surface into 3-space. ...

The "Fifth dimension" in popular culture

• In the fictitious universe of DC Comics, the "Fifth dimension" is the place from which Mister Mxyzptlk comes.
• In 1966, The Byrds released an album titled Fifth Dimension, in which the fifth dimension is a metaphor for unexplored and unknown aspects of the universe and oneself.
• The novel The Boy Who Reversed Himself features four and five-dimensional space, referred to as 4-space and 5-space.
• The hard science fiction novel Diaspora by Greg Egan features a series of ten dimensional universes arrayed inverse to one another, wherein every odd universe has four "macro" dimensions, three space plus one time, and six "submicro" dimensions, manifesting as a 6-sphere per every Planck distance, but which are themselves another ten dimensional universe, featuring six macro dimensions, five space plus one time, and four submicro dimensions per every Planck distance. A substantial portion of the novel depicts daily life and physics in such a universe, which differs substantially due to the peculiar physics hypothesis Egan formulated for the novel.
• Rod Serling's The Twilight Zone television series intro included the line, "There is a Fifth Dimension, beyond that which is known to man."
• In the first episode of Doctor Who, Ian Chesterton was teaching his class about the three dimensions when Susan Foreman, his student and the Doctor's granddaughter, corrected him to say there were in fact five dimensions. He agreed the fourth was time, and asked her about the fifth, to which she replied it was 'space'.
• There is a fictional book, Hyperspace, in a series called 'Choose Your Own Adventure'
• The characters in Madeline L'Engle's novel, "A Wrinkle In Time" use the fifth dimension to travel through space.
• In the children's television program "Mona the Vampire", there is an amusement park ride called the "Fifth Dimensia"
• The "5th Dimension" was a popular soul/pop group in the late 60's starring Marilyn McCoo and Billy Davis and featured such hits as "Wedding Bell Blues", Stoned Soul Picnic", "Up, Up, and Away", "Aquarius", and many others...

DC Comics is an American comic book and related media company. ... Mister Mxyzptlk (roughly pronounced Miks-yez-pit-lik, or Mix-yez-pittle-ik, also nicknamed Mxy) is a fictional supervillain who appears in DC Comics Superman comic books. ... Year 1966 (MCMLXVI) was a common year starting on Saturday (link will display full calendar) of the 1966 Gregorian calendar. ... The Byrds (formed in Los Angeles, California, in 1964) were an American rock band. ... Fifth Dimension is the third album by The Byrds, released in the summer of 1966. ... The Boy Who Reversed Himself (1986) is a science fiction novel by William Sleator. ... Hard science fiction is a category of science fiction characterized by an emphasis on scientific or technical detail, or on scientific accuracy, or on both. ... Diaspora is a hard science fiction novel by Australian writer Greg Egan, published in 1997. ... Greg Egan (August 20, 1961, Perth, Western Australia) is an Australian computer programmer and science fiction author. ... For other uses, see sphere (disambiguation). ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... The Twilight Zone title. ... An Unearthly Child (also known as 100,000 BC, among other titles, see below) is a serial in the British science fiction television series Doctor Who, which was first broadcast in four weekly parts from 23 November to 14 December 1963. ... This article is about the television series. ... Ian Chesterton is a fictional character in the British science fiction television series Doctor Who and a companion of the First Doctor. ... Susan Foreman is a fictional character in the British science fiction television series Doctor Who. ... Madeleine LEngle (b. ... For the movie adaptation, see A Wrinkle in Time (film) . A Wrinkle in Time is a science fantasy[1] novel by Madeleine LEngle, written between 1959 and 1960[2] and published in 1962 after at least 26 rejections by publishers[3] because it was, in LEngles words... Mona the Vampire is an animated childrens television based on the series Mona le Vampire, directed by Louise Piche and Jean Caillon, originally based on the short stories by Sonia Halleyman and Hiawyn Oram. ...

See also

• 5-manifold
• Hypersphere
• Dimension
• Fourth dimension

There are very few or no other articles that link to this one. ... 2-sphere wireframe as an orthogonal projection Just as a stereographic projection can project a spheres surface to a plane, it can also project a 3-spheres surface into 3-space. ... 2-dimensional renderings (ie. ... For other uses, see Fourth dimension (disambiguation). ...

External links

Anaglyph of a five dimensional hypercube in hyper perspective