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| In [[physics]] and [[mathematics]], a [[Euclidean vector|sequence]] of ''n'' [[Real number|numbers]] can also be understood as a [[point (geometry)|location]] in ''n''-dimensional space. When ''n'' = 7, the set of all such locations is called '''7-dimensional Euclidean space'''. Seven-dimensional [[elliptical space|elliptical]] and [[hyperbolic space]]s are also studied, with constant positive and negative curvature.
| | Fantastic your wedding registry with cutting-edge cutlery designed with exceptional Japanese craftsmanship — and add Shun's Classic four-Piece Steak Knife Set to your list of kitchen need to-haves. If you want to use your kitchen knives to chop and slice without the need of your arms finding tired, these are extremely very good selections for you. There are distinct companies of these Japanese kitchen knives but the most effective test to assist you decide on the finest is to attempt it out yourself. Also, some kitchen knives are much more ergonomic than other folks so it is best to locate one particular that is comfy to hold. On the other hand, if you want to use your kitchen knives with a little bit of elbow grease, you can.<br><br><br><br>They will help you tackle chopping jobs on a larger scale than a paring knife will be appropriate for so they are almost certainly 1 of the most critical knives you will will need. A santoku is a multipurpose kitchen knife originating in Japan. It is lighter and shorter with a thinner blade than conventional Western kitchen knives. If the blade rusts, scour to eliminate rust and continue to use. Kershaw nevertheless holds major good quality for hunting knives.<br><br>Naturally, you want to use your knife as it was intended to be employed. Do not attempt to use a paring knife to reduce a difficult spaghetti squash in half, for instance. Use every single knife for the type of task it was designed for, and you will love your knives for a lot of years to come. To cut my spaghetti squashes, which tend to be very challenging, I use a massive, heavy-bladed knife that can withstand the stress necessary. You could have noticed that I didn't say something about the appears of the knives you purchase. For domestic use only.<br><br>Choose the kitchen appliances such as a [http://Browse.Deviantart.com/?q=convection convection] oven, rotisserie unit, grill units and freezer unit to give it a modern taste. Here is more info about [http://www.thebestkitchenknivesreviews.com/best-knife-set-reviews-top-kitchen-sets/ Best Knife Set Quality] look at our web-site. This is the place exactly where all the action occurs and most of the kitchen equipment and apparatus are utilised. Accessorizing your kitchen is crucial to generating your contemporary kitchen great. One more apparent and crucial element to feel about when designing your new kitchen is your cost band.<br><br>Always use a wooden, bamboo or plastic board for chopping on - try to steer clear of using stone, glass or marble as it may perhaps blunt or chip your knife. A knife block will safely hold your knives inside easy access, preventing them from getting chipped or broken. Global knives had been 1st developed in 1985 by Japanese craftsman Minoru Tsuchida. When you use a knife, it becomes an extension of yourself. |
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| Abstract seven-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real [[universe]] in which we live is somehow seven-dimensional (or indeed higher) is a topic that is debated and explored in several branches of physics, including [[astrophysics]] and [[particle physics]], but it does not matter for mathematics.
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| Formally, seven-dimensional [[Euclidean space]] is generated by considering all real 7-[[tuple]]s as 7-[[Euclidean vector|vector]]s in this space. As such it has the properties of all Euclidian spaces, so it is linear, has a [[Metric (mathematics)|metric]] and a full set of vector operations. In particular the [[dot product]] between two 7-vectors is readily defined, and can be used to calculate the metric. 7 × 7 [[matrix (mathematics)|matrices]] can be used to describe transformations such as [[rotation]]s which keep the origin fixed.
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| A distinctive property is that a [[cross product]] can be defined only in three or seven dimensions (see [[seven-dimensional cross product]]). This is due to the existence of [[quaternion]]s and [[octonion]]s.
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| ==Geometry==
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| ===7-polytope===
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| {{Main|7-polytope}}
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| A [[polytope]] in seven dimensions is called a 7-polytope. The most studied are the [[regular polytope]]s, of which there are only [[List_of_regular_polytopes#Convex_4|three in seven dimensions]]: the [[7-simplex]], [[7-cube]], and [[7-orthoplex]]. A wider family are the [[uniform 7-polytope]]s, constructed from fundamental symmetry domains of reflection, each domain defined by a [[Coxeter group]]. Each uniform polytope is defined by a ringed [[Coxeter-Dynkin diagram]]. The [[7-demicube]] is a unique polytope from the D7 family, and [[3 21 polytope|3<sub>21</sub>]], [[2 31 polytope|2<sub>31</sub>]], and [[1 32 polytope|1<sub>32</sub>]] polytopes from the E7 family.
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| {| class=wikitable
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| |+ Regular and uniform polytopes in seven dimensions<BR>(Displayed as orthogonal projections in each [[Coxeter plane]] of symmetry)
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| |-
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| !A<sub>6</sub>
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| !colspan=2|BC<sub>7</sub>
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| !D<sub>7</sub>
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| !colspan=3|[[E7 (mathematics)|E<sub>7</sub>]]
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| |- align=center
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| |[[File:7-simplex t0.svg|altN=7-simplex|120px]]<BR>[[7-simplex]]<BR>{{CDD|node_1|3|node|3|node|3|node|3|node|3|node|3|node}}
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| |[[File:7-cube t0.svg|altN=7-cube|120px]]<BR>[[7-cube]]<BR>{{CDD|node_1|4|node|3|node|3|node|3|node|3|node|3|node}}
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| |[[File:7-cube t6.svg|altN=7-orthoplex|120px]]<BR>[[7-orthoplex]]<BR>{{CDD|node|4|node|3|node|3|node|3|node|3|node|3|node_1}}
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| |[[File:7-demicube t0 D7.svg|120px]]<BR>[[7-demicube]]<BR>{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node}}
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| |[[File:up2 3 21 t0 E7.svg|120px]]<BR>[[3 21 polytope|3<sub>21</sub>]]<BR>{{CDD|nodea_1|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea}}
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| |[[File:up2 2 31 t0 E7.svg|120px]]<BR>[[2 31 polytope|2<sub>31</sub>]]<BR>{{CDD|nodea|3a|nodea|3a|nodea|3a|branch|3a|nodea|3a|nodea_1}}
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| |[[File:up2 1 32 t0 E7.svg|120px]]<BR>[[1 32 polytope|1<sub>32</sub>]]<BR>{{CDD|nodea|3a|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}
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| |}
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| ===6-sphere===
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| The [[n-sphere|6-sphere]] or hypersphere in seven dimensions is the six dimensional surface equidistant from a point, e.g. the origin. It has symbol {{math|''S<sup>6</sup>''}}, with formal definition for the 6-sphere with radius ''r'' of
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| :<math>S^6 = \left\{ x \in \mathbb{R}^7 : \|x\| = r\right\}.</math>
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| The volume of the space bounded by this 6-sphere is
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| : <math>V_7\,=\frac{16 \pi^3}{105}\,r^7</math>
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| which is 4.72477 × ''r''<sup>7</sup>, or 0.0369 of the [[7-cube]] that contains the 6-sphere.
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| ==Applications==
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| ===Physics===
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| ====Non-associative Ashketar gravity====
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| There is a paper on [[non-associativity|Non-associative]] Ashketar gravity or [[Loop quantum gravity]] in seven dimensions.<ref>[http://ci.nii.ac.jp/naid/110004749604/en Paper on CiNii]</ref><ref>[http://nels.nii.ac.jp/els/contents.php?id=ART0007490175&type=pdf&lang=en&host=cinii Part of paper - requires login]</ref>
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| ====String theory and M-theory====
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| [[Image:Calabi-Yau.png|right|thumb|200px|[[Calabi-Yau manifold]] ([[3D projection]])]]
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| {{main|String theory|M-theory}}
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| A key feature of string theory is that, though it is an attempt to model our physical universe, it takes place in a space with more dimensions than the four of spacetime that we are familiar with. In particular a number of string theories take place in a ten dimensional space, adding an extra six dimensions. These extra dimensions are required by the theory, but as they cannot be observed are thought to be quite different, perhaps [[Compactification (physics)|compactified]] so they form a six dimensional space with a [[Calabi–Yau manifold|particular geometry]] too small to be observable. In [[M-theory]], which unifies the five types of string theory, there is a seventh dimension involved.
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| ===Mathematics===
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| ====Cross product====
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| {{main|Seven-dimensional cross product}}
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| As mentioned above, a cross product in seven dimensions analogous to the usual [[Three-dimensional cross product|three]] can be defined, and in fact a cross product can only be defined in three and seven dimensions.
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| ====Exotic sphere====
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| {{main|Exotic sphere}}
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| In 1956, [[John Milnor]] constructed an [[exotic sphere]] in 7 dimensions and showed that there are at least 7 differentiable structures on the 7-sphere. (The number is now known to be 28.)
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| ==See also==
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| *[[Euclidean space]]
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| *[[Euclidean geometry]]
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| *[[7-polytope]]
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| *[[Polytope]]
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| *[[M-theory]]
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| *[[List of geometry topics]]
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| *[[List of regular polytopes]]
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| *[[Exotic sphere]]
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| ==Notes==
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| Seventh dimension discussions are less common than [[five-dimensional space|fifth dimension]] and [[M-theory|eleventh dimension]] theories popularized in [[science]] at the moment by [[mathematicians]] in [[quantum physics]] under [[quantum mechanics]], [[string theory]], and [[quantum gravity]]. This is possibly due in part to stigma of [[time travel]] becoming a popular topic in [[science fiction]], or simply that research has not needed to move in that direction lately.
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| ==References==
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| {{reflist}}
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| {{Dimension topics}}
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| {{DEFAULTSORT:Seven-Dimensional Space}}
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| [[Category:Dimension]]
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| [[Category:Multi-dimensional geometry]]
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Fantastic your wedding registry with cutting-edge cutlery designed with exceptional Japanese craftsmanship — and add Shun's Classic four-Piece Steak Knife Set to your list of kitchen need to-haves. If you want to use your kitchen knives to chop and slice without the need of your arms finding tired, these are extremely very good selections for you. There are distinct companies of these Japanese kitchen knives but the most effective test to assist you decide on the finest is to attempt it out yourself. Also, some kitchen knives are much more ergonomic than other folks so it is best to locate one particular that is comfy to hold. On the other hand, if you want to use your kitchen knives with a little bit of elbow grease, you can.
They will help you tackle chopping jobs on a larger scale than a paring knife will be appropriate for so they are almost certainly 1 of the most critical knives you will will need. A santoku is a multipurpose kitchen knife originating in Japan. It is lighter and shorter with a thinner blade than conventional Western kitchen knives. If the blade rusts, scour to eliminate rust and continue to use. Kershaw nevertheless holds major good quality for hunting knives.
Naturally, you want to use your knife as it was intended to be employed. Do not attempt to use a paring knife to reduce a difficult spaghetti squash in half, for instance. Use every single knife for the type of task it was designed for, and you will love your knives for a lot of years to come. To cut my spaghetti squashes, which tend to be very challenging, I use a massive, heavy-bladed knife that can withstand the stress necessary. You could have noticed that I didn't say something about the appears of the knives you purchase. For domestic use only.
Choose the kitchen appliances such as a convection oven, rotisserie unit, grill units and freezer unit to give it a modern taste. Here is more info about Best Knife Set Quality look at our web-site. This is the place exactly where all the action occurs and most of the kitchen equipment and apparatus are utilised. Accessorizing your kitchen is crucial to generating your contemporary kitchen great. One more apparent and crucial element to feel about when designing your new kitchen is your cost band.
Always use a wooden, bamboo or plastic board for chopping on - try to steer clear of using stone, glass or marble as it may perhaps blunt or chip your knife. A knife block will safely hold your knives inside easy access, preventing them from getting chipped or broken. Global knives had been 1st developed in 1985 by Japanese craftsman Minoru Tsuchida. When you use a knife, it becomes an extension of yourself.