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Truth table for all binary logical operators: added rows Com, L-id, and R-id to the truth value table. They should be here rather than in the key table below so they can be visually checked. Is there another page with a 16 op table?
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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.
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We might be including further assets that may assist you wade via these decisions over time. So you'll want to keep checking again for the newest info. Ultimate Pocket Knife Comparison Information<br><br>A pocket knife that you simply just plan on utilizing on a regular basis is designed for performance just like the Buck Canoe Knife The canoe knife is a classical designed knife These knives normally function customary stainless steel blades and deal with materials ranging from wooden to composite supplies. The Buck canoe knife has a spear blade which is designed for piercing and chopping. If you want a sound, if not the very best, pocket folding knife , listed below are some major steps into choosing one. With slightly bit data, it's possible you'll differentiate an outstanding pocket folding knife from a bad one.<br><br>Pocket knives are not a model new invention. They've discovered these knives courting way back to 600-500BC. All although it is vitally rear to search out one. In ideas days folks used fastened blades. Pocket knives actually said to take off these days. Given that in numerous place it is in direction of the regulation to carry a hard and fast blade knife with you. As a consequence of this Pocket knives really began to make there manner into our lives. Survival knives should be very sturdy. There are many them that have options aside from only a knife blade. Iframe  height="350" width="500"<br><br>In terms of choosing a ‘ Finest Folding Knife ’, we can’t simply ignore Gayle Bradley and go forward to pick one thing else. Gayle Bradley is without doubt one of the main gamers in making customized made folding knife since 1988. Later they partnered themselves with Spyderco. Partnership of those two introduced the revolution as Spyderco are well known to offer tremendous knives and provides greatest finishing touch to every knives. That’s how Spyderco Gayle Bradley Folder knife was born. These two knives maker come collectively and manufactured this rigid, medium framed folding knife in USA.<br><br>If your exercise is wooden-working you might want a knife with 2 or three knives and a screwdriver blade. Knives reminiscent of this resemble a boy scout knife with fewer blades. Are you a hunter or fisherman? If therefore, you defiantly have loads of uses for a pocket knife , corresponding [http://thebestpocketknifereviews.com/best-utility-knife-top-rated-knives-analysis/ superknife Sk2 Folding utility knife] to making ready meals, reducing string, what if your hunting knife fell out of the scabbard whilst you had been searching and is misplaced. How do you need to gut your dog? Knives are perfect for carving and collapsing. With so many sizes and styles there's a pocket knife for all uses.<br><br>Self defense and survival are two things that should never be taken with no consideration. You should not wait till the day when you are mugged by [http://Blacklotusgaming.net/members-2/dericbagwell/activity/186949/ robbers] so that you could be taught the significance of being prepared. It is vitally unlucky that tragedies usually come once we least anticipate. This is the [http://sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=Stanley+nonetheless+makes+an+identical+retractable+fast-change+that%27s+even+made+out+of+metallic%2C+however+despite+the+upper+high+quality+of+material+%28metallic+vs.+plastic%29%2C+it+doesn%27t+hold+the+blade+rigid+%28the+blade+wobbles+barely%29+and+it+would+not+hold+the+blade+secure+%E2%80%93+the+blade+fly%27s+out+of+the+knife+when+scoring+down+a+sheet+of+drywall.%0D%0A%0D%0AThe+short+blade+change+system+can+also+be+very+important+to+effectively+do+your+work+with+out+having+to+take+time+to+swap+out+the+blades.+With+some+utility+knives+it+can+be+extraordinarily+difficult+to+vary+out+the+blades+and+some+utility+knives+actually+require+you+to+make+use+of+a+screwdriver+when+altering+out+the+blades.+With+the+Lenox+Gold+utility+knife+it+literally+solely+takes+a+few+seconds+to+swap+out+the+utility+knife+blade+and+start+using+a+new+one.+You+additionally+get+two+recent+titanium+long+lasting+edges+to+every+blade.+Therefore+you+can+first+simply+pull+out+the+blade+and+turn+it+around+and+then+after+each+edges+are+uninteresting+then+you+may+simply+swap+out+the+blade+for+a+brand+new+blade.%0D%0A%0D%0AThe+KA-BAR%C2%AE+USMC+Preventing%2FUtility+knife+is+known+in+its+own+proper+with+a+historical+background+and+part+of+an+American+legend.+It+measures+12%22+total%2C+with+a+7%22+black+epoxy+powder+coated+1095+excessive+carbon+metal+blade+with+a+blood+groove.+It+has+a+polished+stacked+leather-based+handle+with+black+epoxy+powder+coated+carbon+steel+guard+and+butt+cap.+Comes+with+a+black+glass+stuffed+nylon+sheath+with+multiple+put+on+options.+Customary+Edge+Only.+This+fastened+blade+knife+from+the+Home+of+Irwin+is+a+perfect+specimen+in+its+class.+It+has+a+slim+nostril%2C+and+is+good+for+scoring.+Its+ergonomic+shape+makes+it+price+each+penny.+It+additionally+comes+with+a+set+off+grip+for+%E2%80%98reducing+on+the+pull%27.+It%27s+quite+snug+to+use%2C+even+with+most+heavy+obligation+woodwork.%0D%0A%0D%0AWhether+it%27s+a+chef%27s+knife%2C+utility+knife%2C+Steak+knife+or+paring+knife%2C+there+is+some+fundamental+and+stuck+things+that+every+of+these+knives+ought+to+capable+of+fulfil+as+soon+as+we+purchase+those+knife+to+make+use+of+in+our+each+day+life.+We+are+identified+some+features+that+each+kitchen+knife+must+fulfil+and+it%27s+as+follows+%E2%80%93+I+choose+plastic+utility+knives+as+a+result+of+they+are+generally+lighter+in+weight%2C+and+the+least+expensive.+If+you+wish+to+spend+a+bit+of+more+cash%2C+and+get+something+with+a+little+bit+more+heft%2C+a+%5Bhttp%3A%2F%2FWww.Dict.cc%2Fenglisch-deutsch%2Fmetallic-cased%2Butility.html+metallic-cased+utility%5D+knife+is+what+you%27ll+need.+That+is+pretty+much+the+key.+Extremely-skinny+and+extremely+mild.+That+is+true+utility.+A+kitchen+knife+that+actually+feels+prefer+it+slides+via+meals+like+butter.+Fowl%27s+Beak+Knife++Boning+Knife++Butter+Knife++Ceramic+Knife%0D%0A%0D%0ABlade+Changing+%E2%80%93+this+time+seven+of+the+eight+featured+fast+release+blade+mechanisms%2C+the+Irwin+fastened+blade+intentionally+didn%27t+obviously.+Of+the+opposite+seven+it+is+vitally+difficult+to+choose+a+winner+however+most+likely+the+one+that+may+be+the+quickest+can+be+the+Bostitch+as+the+discharge+is+on+the+top+next+to+the+retract+lever.+We+could+additionally+nonetheless+see+how+it+is+perhaps+the+simplest+to+by+chance+press+whereas+in+use.+In+comparision+to+just+a+few+years+again+now+we+have+to+say+all+had+been+actually+quick%2C+most+likely+none+took+over%C2%A06+seconds+which+is+wonderful+to+assume%C2%A0such+a+short+while+in+the+past%C2%A0and+fumbling+around+with+this.+%E2%80%93+Bostitch%0D%0A%0D%0AUse+one+of+the+newer+model+self-retracting+blade+knives.+The+technology+has+elevated+the+security+of+this+instrument+tremendously+over+the+previous+several+years.+This+knife+is+for+survival%2C+which+implies+it+has+to+be+adaptable+and+work+in+many+alternative+situations.+It+must+be+big+enough+to+get+the+job+achieved%2C+however+not+so+bulky+that+it%27s+a+burden+to+carry.+Most+importantly%2C+it+needs+to+be+sturdy.+Finally%2C+be+sure+the+size+of+the+blade+is+appropriate+on+your+adventures.+You+don%27t+want+something+too+heavy+or+impractically+large.+You+desire+a+knife+that+you+need+to+use+to+perform+detailed+work+like+skinning+an+animal.+Most+individuals+suggest+something+between+four+and+seven+inches.+There+are+4+widespread+sorts+of+blade+edges+available+on+business+cutlery.+Straight+Edge%0D%0A%0D%0AThis+folding+razor+knife+is+accredited+for+army+use+and+is+issued+NSN+6515-01-363-1212.+It%27s+manufactured+below+MilSpec+MIL-R-365408%2C+thus+making+it+a+very+top+quality+merchandise.+Do+not+be+fooledby+the+Folding+Utility+Knife%27s+low+worth.+Sheffield+makes+a+really+elegant+utility+knife+that+holds+a+blade+very+inflexible%2C+just+secure+sufficient%2C+and+blade+adjustments+are+virtually+as+fast+as+the+standard+%E2%80%9Cfast+change%E2%80%9D+fashions.+However%2C+the+knife+doesn%27t+have+any+capability+for+blade+storage.+It+additionally+folds+as+an+alternative+of+retracts%2C+which+in+certain+conditions%2C+can+be+considerably+of+a+nuisance.+In+Australia%2C+it+is+unlawful+to+promote+a+reducing+implement+equivalent+to+a+utility+knife+to+anybody+underneath+16+years+of+age%2C++citation+needed++and+proof+of+age+is+usually+demanded+of+purchasers.+Santoku+Knife%0D%0A%0D%0ASerrated+Knife++Slicing%2FCarving+Knife++Steak+Knife++Tomato+Knife++Utility+Knife+Check+All+Common+Utility+Knives+on++Evaluations+of+Prime+Rated+Utility+Knives+In+The+Market+At+this+time+Milwaukee+48-22-1902+Fastback+II+Flip+Utility+Knife+With+Storage+Reviews+%2C+Find+out+how+to+Put+a+Blade+on+a+Stanley+Utility+Knife+Milwaukee+forty+eight-22-1902+Fastback+II+Flip+Utility+Knife+With+Storage+Video+DeWalt+Folding+DWHT10035L+Utility+Knife+%28%2411%2C+Amazon%29+the+most+recent+addition+to+our+ever+growing+collection+of+utility+knives+this+folding+utility+knife+has+a+number+of+unique+options+together+with+on-board+blade+storage+and+retract+capacity.++In+case+you+loved+this+short+article+and+you+would+want+to+receive+more+details+regarding+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fbest-utility-knife-top-rated-knives-analysis%2F+sheffield+folding+Utility+knife%5D+i+implore+you+to+visit+our+own+web+site.+Both+these+features+enable+the+knife+to+function+simply+as+any+regular+utility+knife+however+in+about+half+the+scale+when+closed.+Also+contains+a+wire+stripper.+5%2F5+%5Bhttp%3A%2F%2Fwww.Google.Co.uk%2Fsearch%3Fhl%3Den%26gl%3Dus%26tbm%3Dnws%26q%3DUtility%26gs_l%3Dnews+Utility%5D+Knife+5+5.ninety+nine&create=Create reason it's] best [http://en.wikipedia.org/wiki/Pocket_knife military knife] to at all times have the perfect pocket knife with you where ever you go. It isn't necessarily for self defense. One of the best knife can serve you in different events, while you unfastened your method in the forest, and likewise when you're about to be attacked by wild animals and even by hostile individuals.<br><br>Make sure to examine your local legal guidelines, particularly if you're planning to [http://Sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=During+an+emergency%2C+an+incredible+utility+knife+is+price+its+weight+in+gold.+Whether+or+not+you+are+looking+for+a+set+blade+utility+knife+on+your+Bug+Out+Bag%2C+Get+Residence+Bag%2C+or+for+your+residence+emergency+gear%2C+a+Mora+Knife+is+a+superb+knife+to+fill+the+invoice.%0D%0A%0D%0AThe+sharp+and+lightweight+paring+knife+is+sort+of+a+miniature+chef%27s+knife%2C+preferrred+for+intricate+tasks+resembling+peeling%2C+deveining+shrimp%2C+seeding+peppers%2C+or+carving+detailed+garnishes.+The+Nakiri+cleaver+is+a+%5Bhttp%3A%2F%2FWww.Danielasandoni.it%2Fcontent%2Fsuperknife-sk2-folding-utility-knife+Japanese+vegetable%5D+knife.+The+skinny+blade+differs+from+the+thick+blade+of+a+traditional+cleaver%2C+so+the+Nakiri+should+not+be+used+for+reducing+meat+or+bones.+The+straight+blade+is+perfect+for+simply+slicing+via+greens+with+only+downward+stress%E2%80%94no+slicing+movement+vital%E2%80%94to+create+straight%2C+even+slices+each+time.+of+the+time+I+take+advantage+of+a+folding+one.+I+really+liked+the+original%2C+chiep+Sheffield%2C+but+have+since+changed+over+to+a+bigger+model+from+Lowes%2C+mainly+because+the+Lowes+mannequin+has+a+belt+clip.+M2+metal+knives+are+discontinued+by+Benchmade.+A2%0D%0A%0D%0AA+knife+used+to+chop+slices+of+cooked+or+smoked+meat%2C+poultry+and+fish.+There+are+numerous+varieties+of+slicing+knives%2C+which+range+in+blade+width%2C+blade+length%2C+flexibility%2C+pointed+to+rounded+suggestions%2C+and+kind+of+leading+edge.+The+construction+of+the+knife+depends+upon+its+use.+Incessantly+the+phrases+slicing+knife+and+carving+knife+are+used+interchangeably%2C+but+the+carving+knife+is+actually+a+wide+range+of+slicing+knife.++If+you+have+any+sort+of+inquiries+concerning+where+and+the+best+ways+to+use+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fbest-utility-knife-top-rated-knives-analysis%2F+thebestpocketknifereviews.Com%5D%2C+you+can+contact+us+at+the+internet+site.+Some+widespread+slicing+knives+are+proven+under.%0D%0A%0D%0AAnother+safety+concern+is+that+it%27s+doable+to+put+a+retractable+in+your+pocket+with+a+bit+little+bit+of+the+blade+peeking+out.+I%27ve+gotten+plenty+of+sharp+pokes+over+time+from+this+taking+place.+These+sorts+of+things+really+can%27t+occur+with+folding+knives.+They%27re+either+open+or+closed+and+there%27s+no+mistaking+which+one+it%27s.+Also%2C+the+slide+mechanism+itself+could+cause+issues.+In+keeping+with+Lyman%2C+%E2%80%9CI%27ve+never+used+a+retractable+with+a+mechanism+that+does+not+ultimately+get+actually+crud-stuffed+and+clunky.+I+positively+favor+folding.%E2%80%9D+My+experience+echoes+this.+It+seems+that+no+matter+how+high+the+standard%2C+over+time+the+blade+slide+becomes+gunked+up%2C+The+blade+is+made+to+interrupt+off+at+the+tip+of+the+blade+when+the+sting+has+gotten+boring.%0D%0A%0D%0AKnives+ought+to+all+the+time+be+saved+as+sharp+as+potential%E2%80%93extra+on+this+later.+Working+with+a+boring+knife+causes+one+to+make+use+of+extra+strain%2C+which+will+increase+the+chance+of+the+blade+slipping+while+slicing.+I+desire+to+at+all+times+work+on+a+wood+or+plastic+reducing+board.+A+majority+of+these+surfaces+give+to+the+blade+versus+a+glass+or+ceramic+floor%2C+which+helps+retain+the+edge.+After+all%2C+you+all+the+time+want+to+minimize+away+from+your+body.+Like+most+of+my+dearer+cookware%2C+I+want+handy+wash+and+dry+my+knives+as+a+substitute+of+utilizing+the+dishwasher.+This+ensures+that+the+knives+are+usually+not+damaged+should+they+come+in+contact+with+different+objects.+Lastly%2C+all+the+time+retailer+knives+in+a+knife+block+or+secure+tray+when+not+in+use.%0D%0A%0D%0ATo+get+the+full+range+of+use+out+of+the+knife+and+as+a+lot+safety+and+portability+as+doable%2C+we+suggest+going+with+the+folding+model+over+the+retractable.+They%27re+smaller+to+store%2C+have+a+tendency+to+come+with+belt+hooks%2C+and+due+to+the+way+in+which+the+folded+blade+nests+in+the+physique%2C+there%27s+a+lower+probability+of+their+accidentally+deploying+in+your+pocket.+Retractable+knives+are+good%2C+however+their+function+set+is+extra+geared+towards+the+skilled+tradesman.+Some+retractable+knives%2C+like+this+Snap-on+%2C+have+a+security+change+that+needs+to+be+flipped+earlier+than+putting+the+knife+in+your+pocket%2C+but+why+hassle+dealing+with+a+two-step+course+of+when+the+double-locking+folding+type+guarantees+that+there+will+not+be+any+in-pocket+mishaps+simply+by+closing+the+knife%3F%0D%0A%0D%0AButcher+knives+usually+have+heavy%2C+extensive%2C+and+barely+curved+blades+which+are+useful+for+cutting%2C+sectioning%2C+and+trimming+giant+pieces+of+meat.+Breaking+knives+are+just+like+butcher+knives+and+are+primarily+used+to+interrupt+down+large+items+of+meat+into+smaller+cuts.+Their+blades+are+normally+around+10%E2%80%9D+and+are+curved+to+create+leverage+to+break+via+tough+pores+and+skin%2C+cartilage%2C+and+small+bones.+They%27re+also+glorious+knives+for+trimming+fats+off+of+meat.+Flank+and+shoulder+knives+are+a+type+of+boning+knife+that+are+glorious+for+creating+flank+steaks.+Their+straight%2C+stiff+blades+are+excellent+for+producing+exact+cuts+whereas+boning%2Cand+jointing.+Chef%27s+-+use+as+a+miniature+cook%27s+knife.+Use+a+large+boning+knife+for+rooster+and+pork.%0D%0A%0D%0AThe+knife+is+designed+in+order+that+it+can+be+opened+and+closed+very+quickly+with+one+hand+and+lock+in+both+position.+The+grip%2C+significantly+the+massive+forefinger+notch%2C+ensures+that+the+knife+will+not+slip+out+of+your+hands%2C+and+the+software+has+a+nice%2C+simple+blade+change+and+a+versatile+belt+hook.+The+Fastback+II+also+has+an+added+gut+hook%2C+so+you%27ll+be+able+to+cut+string+or+open+a+bag+of+chicken+seed+without+ever+unfolding+the+knife+and+exposing+the+blade.+The+deal+with+also+has+room+to+retailer+an+additional+blade.+None+of+the+other+knives+had+such+a+complete+set+of+features.&create=Create purchase] one [http://Voipservicedirectory.com/forums/index.php?a=member&m=2071989 on-line]. For many of us pocket knives are solely helpful instruments, however they could be used as weapons too. So, nowadays they face several authorized restrictions. The size of the blade is prone to be regulated in some states, turning unlawful [http://Www.Thebestpocketknifereviews.com/best-utility-knife-top-rated-knives-analysis/ sheffield folding utility knife] to hold around pocket knives with a blade larger than a sure measurement. The same may occur with certain sorts of pocket knives , you need to have particular care with switchblades as a result of they are the probably to be banned.
 
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.
 
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&nbsp;×&nbsp;7 [[matrix (mathematics)|matrices]] can be used to describe transformations such as [[rotation]]s which keep the origin fixed.
 
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.
 
==Geometry==
===7-polytope===
{{Main|7-polytope}}
 
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.
 
{| class=wikitable
|+ Regular and uniform polytopes in seven dimensions<BR>(Displayed as orthogonal projections in each [[Coxeter plane]] of symmetry)
|-
!A<sub>6</sub>
!colspan=2|BC<sub>7</sub>
!D<sub>7</sub>
!colspan=3|[[E7 (mathematics)|E<sub>7</sub>]]
|- align=center
|[[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}}
|[[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}}
|[[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}}
|[[File:7-demicube t0 D7.svg|120px]]<BR>[[7-demicube]]<BR>{{CDD|nodes_10ru|split2|node|3|node|3|node|3|node|3|node}}
|[[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}}
|[[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}}
|[[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}}
|}
 
===6-sphere===
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
 
:<math>S^6 = \left\{ x \in \mathbb{R}^7 : \|x\| = r\right\}.</math>
 
The volume of the space bounded by this 6-sphere is
 
: <math>V_7\,=\frac{16 \pi^3}{105}\,r^7</math>
 
which is 4.72477 × ''r''<sup>7</sup>, or 0.0369 of the [[7-cube]] that contains the 6-sphere.
 
==Applications==
===Physics===
====Non-associative Ashketar gravity====
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>
 
====String theory and M-theory====
[[Image:Calabi-Yau.png|right|thumb|200px|[[Calabi-Yau manifold]] ([[3D projection]])]]
{{main|String theory|M-theory}}
 
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.
 
===Mathematics===
====Cross product====
{{main|Seven-dimensional cross product}}
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.
 
====Exotic sphere====
{{main|Exotic sphere}}
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.)
 
==See also==
*[[Euclidean space]]
*[[Euclidean geometry]]
*[[7-polytope]]
*[[Polytope]]
*[[M-theory]]
*[[List of geometry topics]]
*[[List of regular polytopes]]
*[[Exotic sphere]]
 
==Notes==
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.
 
==References==
{{reflist}}
 
{{Dimension topics}}
 
{{DEFAULTSORT:Seven-Dimensional Space}}
[[Category:Dimension]]
[[Category:Multi-dimensional geometry]]

Revision as of 23:12, 7 February 2014



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