Meel Euclidean: Qeexidda, guryaha, calaamadaha

Xitaa dugsiga, ardayda oo dhan waxaa lagu soo bandhigay fikirka ah "geometry Euclidean", qodobada ugu muhiimsan ee kuwaas oo diiradda a axioms yar ku salaysan xubno joomateri sida dhibcood, diyaaradaha, dhaqdhaqaaqa si toos ah line. Dhammaantood shirqool ku wada sameeyaan waxa hore u ogaan lahaa by ereyga "meel Euclidean".

Euclidean bannaan, qeexidda oo ku salaysan jagada isku dhufashada scalar of fallaadhaha waa kiis gaar ah oo toosan bannaan (affine), oo dhergiyaa tiro ka mid ah shuruudaha. Marka hore, wax soo saarka gudaha ee fallaadhaha gabi ahaanba waa symmetrical, ie dulinka la wadataa (x, y) marka la eego tirada waa inay isku dulinka la wadataa (y; x), laakiin ka soo horjeeda in jihada.

Marka labaad, haddii ay dhacdo in lagu sameeyo sheyga scalar ee dulinka laftiisa la, natiijada tallaabo tani waxay noqon doontaa wanaagsan. marka laga reebo kaliya noqon lahaa kiiska marka laga bilaabo iyo wadataa afjaridda ee dulinka tani waa loo siman yahay si eber, haddii ay taasi iyo wax soo saarka laftiisa la isku noqon doontaa eber.

Saddexaad, waxaa jira wax soo saarka scalar waa furfurista, ie suuragalnimada in la ballaariyo mid ka mid ah wadataa ay wadarta labada qiimaha aan wuxu wixii isbeddel ah ee natiijada kama dambaysta ah ee isku dhufashada scalar of fallaadhaha. Ugu dambeyntii, in kii afraad, in isku dhufashada ee fallaadhaha by isla qiimaha dhabta ah ee ay wax soo saarka scalar ayaa sidoo kale kordhay arrin isku mid ah.

Haddii ay sidaa tahay, haddii oo dhan afar xaaladaha, waxaan odhan karaa in tani ay tahay meel Euclidean.

meel Euclidean ka dhibic la taaban karo of view, waa la gartaa karo by tusaalooyinka gaarka ah ee soo socda:

1. Kiiska fudud - waa helitaanka set oo ah fallaadhaha qaar ka mid ah shuruucda aasaasiga ah ee joomateri, sheyga scalar.
2. meel Euclidean waa la helay kiiska, haddii by fallaadhaha waxaan uga jeednaa a set uguna qaar ka mid ah tirada dhabta ah la formula la siiyo, isagoo ku tilmaamay in ay wadarta scalar ama wax soo saarka.
3. kiiska A gaarka ah ee meel Euclidean waa lagama maarmaan in la aqoonsado wax-u eber meesha bannaan ee, kaas oo la helay ay dhacdo in dhererka labada fallaadhaha scalar waa eber.

meel Euclidean uu leeyahay tiro ka mid ah guryaha gaarka ah. Waa midda koowaade, factor scalar waxaa laga yaabaa in labada qooys hore iyo factor labaad ee alaabta scalar, natiijada of this ma mari doona wixii isbeddel ah. Marka labaad, oo ay la socdaan xubin ugu horeysay ka qaybinta sheyga scalar, dhaqmo iyo Distributivity element labaad. Waxa intaa dheer in wadarta scalar of fallaadhaha, Distributivity leedahay meel ay dhacdo goynta ah fallaadhaha. Ugu dambeyntii, markii saddexaadna qaar, in isku dhufashada scalar ee dulinka ah si eber, natiijada sidoo kale jiri doona eber.

Sidaas darteed, meel Euclidean - waa fikradda joomatari ugu muhiimsan ee loo adeegsado xalinta dhibaatooyinka la heshiis ah labada dhinac ee fallaadhaha qaraabo in kasta oo kale, waayo, sifooyinka kuwaas oo fikrad sida loo isticmaalo wax soo saarka gudaha.