Euclidean nzvimbo: tsanangudzo, zvivako, zviratidzo

Kunyange kuchikoro, vadzidzi vose nezvevanakomana pfungwa "Euclidean geometry", chikuru zvokudya izvo akaisa pfungwa dzakapoteredza axioms shoma kwakavakirwa geometric zvinhu zvakadai pfungwa, ndege, yakananga mutsetse kufamba. Vose pamwe chete kuumba zviri kare anozivikanwa okuti "Euclidean nzvimbo".

Euclidean nzvimbo, tsanangudzo iyo inobva nzvimbo scalar chokuwanziridza pakati vectors ndiyo nyaya inokosha Linear (affine) nzvimbo, iyo zvinogutsa wandei zvaanoda. Chekutanga, yomukati yemudzimu vectors zirokwazvo zvakafanana, ichibata, kureva Vector pamwe Coordonatele (x; Y) panyaya kwazvo ndiyo akafanana kuti Vector pamwe Coordonatele (Y; x), asi pakatarisana nenhungamiro.

Chechipiri, pane chiitiko kuti akaita scalar zvibereko Vector pachawo, mugumisiro chiito ichi chichava zvakanaka. The chete Kusara zvingaitika kana pokutangira uye kuzviuraya Coordonatele ose Vector ichi akaenzana razero: mune iyi uye chigadzirwa chayo pachawo chete vachava razero.

Chechitatu, pane scalar chigadzirwa riri distributive, kureva mukana kuwedzera mumwe Coordonatele pamusoro Verengai maviri tsika kuti urege kunotoreva shanduko chero wokupedzisira Mugumisiro scalar chokuwanziridza pakati vectors. Pakupedzisira, muna wechina, ari chokuwanziridza pamusoro vectors neMweya iwoyu ukoshi chaihwo dzavo scalar chigadzirwa iri yakawedzera chete chinhu.

Pakadaro, kana zvose zvina ezvinhu aya, tinogona zvakachengeteka kutaura kuti ichi chinhu Euclidean nzvimbo.

Euclidean nzvimbo kubva inoshanda nemaonero, zvinogona dzinoratidzwa inotevera mienzaniso yakananga:

1. The nyore nyaya - ndiye Kuwanikwa yakatarwa pakati vectors nevamwe mitemo inokosha geometry, ari scalar chigadzirwa.
2. Euclidean nzvimbo inotengwa panyaya, kana nokuda vectors isu kureva imwe finite akagadzirwa chaiyo nhamba ane kupiwa yemaitiro, vakarondedzera kwavo scalar mari kana chigadzirwa.
3. A nyaya inokosha ine Euclidean nzvimbo zvinokosha kuziva inonzi razero nzvimbo, iyo yakawanikwa mune chiitiko kuti kureba vaviri scalar vectors ndiyo razero.

Euclidean nzvimbo ine zvakawanda chaiwo zvivako. Chekutanga, scalar chingave kutorwa zvose wokutanga chikomboredzo uye chinhu pamusoro scalar chigadzirwa wechipiri, nemhaka iyi haangavi chaidzo chero kuchinja. Chechipiri, pamwe wokutanga nhengo kubva kuparadzira scalar chigadzirwa, anoita uye Distributivity chinhu chechipiri. Kuwedzera kune scalar Verengai vectors, Distributivity ane nzvimbo nyaya kubvisa kuna vectors. Pakupedzisira, Chechitatu, mune scalar chokuwanziridza pamusoro Vector kuti zero, mugumisiro achava razero.

Nokudaro, Euclidean nzvimbo - inonyanya kukosha geometrical pfungwa inoshandiswa kugadzirisa matambudziko pamwechete yakawiriranwa urongwa vectors hama nepedyo, nokuti hunhu iyo pfungwa yakadaro rinoshandiswa sezvo yomukati chigadzirwa.