|
|
| Line 1: |
Line 1: |
| {{About|the hypothetical extra dimension|the musical group|The 5th Dimension}}
| | I am Oscar and I completely dig that title. To gather coins is one of the issues I love most. Bookkeeping is her working day occupation now. Her family members life in Minnesota.<br><br>my web site ... [http://xrambo.com/blog/191590 home std test kit] |
| [[File:Penteract projected.png|thumb|A [[perspective projection]] 3D to 2D of [[stereographic projection]] 4D to 3D of [[Schlegel diagram]] 5D to 4D|240px]]
| |
| In [[physics]] and [[mathematics]], a [[tuple|sequence]] of ''N'' [[real numbers|numbers]] can be understood to represent a [[coordinate system|location]] in an ''N''-dimensional [[Euclidean space|space]].
| |
| | |
| Abstract '''five-dimensional space''' occurs frequently in mathematics, and is a 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]].
| |
| | |
| In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three [[space|spatial]] dimensions and one [[time]] dimension of [[Relativity (physics)|Relativity]]. The [[Kaluza–Klein theory]] used the fifth dimension to unify [[gravity]] with the [[electromagnetic force]]; e.g. [[Minkowski space]] and [[Maxwell's equations#In vacuum|Maxwell's equations in vacuum]] can be embedded in a five-dimensional [[Riemann curvature tensor]]. Kaluza–Klein theory today is seen as essentially a [[gauge theory]], with [[gauge group]] the [[circle group]]. [[M-theory]] suggests that [[space–time]] has 11 dimensions, seven of which are "rolled up" to below the subatomic level. Physicists 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 force]]s.
| |
| | |
| 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 dimension''. 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 path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the ''spacetime fabric''.
| |
| | |
| ==Five-dimensional geometry==
| |
| ===Polytopes===
| |
| | |
| {{Main|5-polytope}}
| |
| | |
| In five or more dimensions, only three [[regular polytope]]s exist. In five dimensions, they are:
| |
| | |
| # The '''[[5-simplex]]''' of the [[simplex]] family, with 6 vertices, 15 edges, 20 faces (each an [[equilateral triangle]]), 15 cells (each a regular [[tetrahedron]]), and 6 hypercells (each a [[5-cell]]).
| |
| # The '''[[5-cube]]''' of the [[hypercube]] family, with 32 vertices, 80 edges, 80 faces (each a [[Square (geometry)|square]]), 40 cells (each a [[cube]]), and 10 hypercells (each a [[tesseract]]).
| |
| # The '''[[5-orthoplex]]''' of the [[cross polytope]] family, with 10 vertices, 40 edges, 80 faces (each a [[triangle]]), 80 cells (each a [[tetrahedron]]), and 32 hypercells (each a [[5-cell]]).
| |
| | |
| A fourth polytope can be constructed as an [[Alternation (geometry)|alternation]] of the 5-cube, and is called a '''5-demicube''', with half the vertices (16), bounded by alternating [[5-cell]] and [[16-cell]] hypercells.
| |
| | |
| {| class=wikitable
| |
| |+ Regular and semiregular polytopes in five dimensions<br>(Displayed as orthogonal projections in each [[Coxeter plane]] of symmetry)
| |
| |-
| |
| !A<sub>5</sub>
| |
| !colspan=2|BC<sub>5</sub>
| |
| !D<sub>5</sub>
| |
| |- align=center
| |
| |[[File:5-simplex t0.svg|altN=5-simplex|120px]]<br>[[5-simplex]]<br>{{CDD|node_1|3|node|3|node|3|node|3|node}}
| |
| |[[File:5-cube t0.svg|altN=5-cube|120px]]<br>[[5-cube]]<br>{{CDD|node_1|4|node|3|node|3|node|3|node}}
| |
| |[[File:5-cube t4.svg|altN=5-orthoplex|120px]]<br>[[5-orthoplex]]<br>{{CDD|node|4|node|3|node|3|node|3|node_1}}
| |
| |[[File:5-demicube t0 D5.svg|120px]]<br>[[5-demicube]]<br>{{CDD|nodes_10ru|split2|node|3|node|3|node}}
| |
| |}
| |
| | |
| The 5-simplex is self-[[dual polyhedron#Dual polytopes|dual]], and the 5-cube and 5-orthoplex are dual to each other. The 5-demicube can be constructed by removing alternate vertices of the 5-cube.
| |
| | |
| The following are three projected images of the edges of a [[5-cube]]:
| |
| {| class="wikitable"
| |
| |-
| |
| |[[File:2d of 5d 1.jpg|200px]]
| |
| |[[File:2d of 5d 2.jpg|200px]]
| |
| |[[File:2d of 5d 3.svg|200px]]
| |
| |}
| |
| | |
| === Hypersphere ===
| |
| A [[hypersphere]] in 5-space (also called a '''4-sphere''' due to its surface being 4-dimensional) consists of the set of all points in 5-space at a fixed distance ''r'' from a central point P. The hypervolume enclosed by this hypersurface is:
| |
| :<math>V=\frac{8\pi ^2r^5}{15}</math>
| |
| | |
| ==In popular culture==
| |
| In popular usage, the "fifth dimension" is often used to refer to unexplored or unknown aspects of the universe, and not necessarily to the mathematical concept of a 5-dimensional space. For example, the opening narration of ''[[The Twilight Zone]]'' begins: "There is a fifth dimension, beyond that which is known to man." In the fictional universe of [[DC Comics]], the "fifth dimension" is said to be the place from which [[Mister Mxyzptlk]], a Superman villain, comes. The 1965 ''[[Lost in Space]]'' TV show episode “Invaders from the Fifth Dimension” features hostile aliens from the fifth dimension, and the [[Robot B-9|Robot]] describes their spaceship by saying: “The craft is surrounded by a force field in the fifth dimension, which is... mathematically... impossible.” In 1966, [[The Byrds]] released an album titled ''[[Fifth Dimension (album)|Fifth Dimension]]'', using the fifth dimension as a metaphor for unexplored and unknown aspects of the universe and oneself. [[The 5th Dimension]] is the name of an American vocal music group popular in the late 1960s and early 1970s. In [[Hindu]] philosophy, the fifth dimension of love of the Divine is termed by the Gaudiya Vaisnavas as [[turiya|turyatita]], the dimension of the soul's Soul. The original ''[[Doctor Who]]'' episode hints at the 5th dimension being key to the abilities of the TARDIS.{{Citation needed|date=November 2009}}
| |
| | |
| Other uses of the "fifth dimension" are closer to its mathematical meaning. For example, the novel ''[[The Boy Who Reversed Himself]]'' features 4-dimensional and 5-dimensional spaces, using the mathematical fact that a 3-dimensional object can be turned into its mirror image if additional spatial dimensions were available for it to rotate through. The characters in [[Madeleine L'Engle]]'s novel ''[[A Wrinkle In Time]]'' use the fifth dimension{{citation needed|date=March 2010|reason=5th spatial dimension?}} as a "dimensional shortcut" to travel through space. A similar concept appears in the [[Powerpuff Girls]] episode ''Bring Back Jojo'', where a creature able to see higher dimensions takes a dimensional shortcut through a fifth dimension to travel through time. The ''[[Red Dwarf]]'' episode [[Parallel Universe (Red Dwarf)|"Parallel Universe"]] refers to the fifth dimension as the space in which multiple four-dimensional spaces exist.
| |
| | |
| Not all references to the "fifth dimension" in the mathematical sense involve time travel or space travel; [[Douglas Adams]]' book ''Mostly Harmless'' advances the idea of the fifth dimension being probability.
| |
| | |
| In [[Mikhail Bulgakov]]'s [[The Master and Margarita]], valet Koroviev in an explanation to Margarita attributes the expansion of a small apartment into the size of a large auditorium to the fifth dimension.
| |
| | |
| In the "original" or "boxed" version of the [[Dungeons & Dragons]] roleplaying game rulebooks (discontinued in 2000), consisting of the Basic set, and then the Expert, Companion, Master and Immortals expansion sets, a five-dimensional model was proposed in the Masters set where characters from the ordinary plane had the first, second and third dimensions as their three-dimensional home, but other-dimensional beings called the third, fourth and fifth dimension home. Upon perceiving each other, each thought the other kind to be horribly deformed "demons".
| |
| | |
| In ''[[Family Guy]]'', [[Mayor Adam West]] sends Alex Trebek, host of ''Jeopardy'', to the fifth dimension by making him say his name backwards, commenting, "Only saying his name backwards can send him back to the fifth dimension where he belongs." This is a parody of Mr. Mxyzptlk's weakness in the Superman comics.
| |
| | |
| In a well-received 2010 CBS commercial for ''[[How I Met Your Mother]]'', ''[[Accidentally on Purpose (TV series)|Accidentally on Purpose]]'', ''[[Two and a Half Men]]'', ''[[The Big Bang Theory]]'', and the ''[[Late Show with David Letterman]]'', an announcer states that "Everyone has 3-D, but only CBS has comedy in 5-D." This was a reference to the growing popularity of [[4-D film]] in the later half of 2009, suggesting that certain programs on CBS feature 5-dimensional effects. By the end of the commercial, however, it is revealed that the letter [[D]] in 5-D does not stand for "Dimension," but stands for "Delightful, Delicious, Daring, Demented, and Dave."<ref> [[Hermann Weyl|Weyl, Hermann]], ''[http://www.archive.org/details/raumzeitmateriev00weyl Raum, Zeit, Materie]'', 1918. 5 edns. to 1922 ed. with notes by Jūrgen Ehlers, 1980. trans. 4th edn. Henry Brose, 1922 ''[http://www.archive.org/details/spacetimematter00weyluoft Space Time Matter]'', Methuen, rept. 1952 Dover. ISBN 0-486-60267-2.</ref>
| |
| | |
| ==See also==
| |
| *[[Higher dimension]]
| |
| *[[5-manifold]]
| |
| *[[List of regular polytopes#Convex 4|List of regular 5-polytopes]]
| |
| *[[Hypersphere]]
| |
| *[[Dimension]]
| |
| | |
| ==Further reading==
| |
| *{{cite book |title=Space-Time-Matter, Modern Kaluza-Klein Theory |last=Wesson |first=Paul S. |authorlink= |coauthors= |year=1999 |publisher=World Scientific |location=Singapore |isbn=981-02-3588-7 |pages= }}
| |
| *{{cite book |title=Five-Dimensional Physics: Classical and Quantum Consequences of Kaluza-Klein Cosmology |last=Wesson |first=Paul S. |authorlink= |coauthors= |year=2006 |publisher=World Scientific |location=Singapore |isbn=981-256-661-9 |pages= }}
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://robertinventor.com/software/virtualflower/virtualflower/tesseract.htm Anaglyph of a five dimensional hypercube in hyper perspective]
| |
| | |
| {{Dimension topics}}
| |
| | |
| [[Category:Dimension]]
| |
| [[Category:Multi-dimensional geometry]]
| |
I am Oscar and I completely dig that title. To gather coins is one of the issues I love most. Bookkeeping is her working day occupation now. Her family members life in Minnesota.
my web site ... home std test kit