Euclidean sarari: definition, Properties, ãyõyi

Ko da a cikin makaranta, duk dalibai suna gabatar da manufar "Euclidean lissafi", babban arziki da wanda ake mayar da hankali a kusa da 'yan axioms bisa lissafi da abubuwa kamar maki, jirage, madaidaiciya line motsi. Dukan su tare da nunawa abin da aka riga aka sani da Kalmar "Euclidean sarari".

Euclidean sarari, da definition wanda dogara ne a kan matsayi na scalar multiplication na vectors ne na musamman hali na mikakke (affine) sarari, wanda kosad da yawan bukatun. Da fari dai, na ciki samfurin na vectors shi ne cikakken tsakaitã, watau vector tare da tsarawa (x; y) a cikin sharuddan na awo ne m ga vector tare da tsarawa (y; x), amma daura da a shugabanci.

Abu na biyu, a yayin da cewa sanya scalar samfurin na vector da kanta, da sakamakon wannan mataki zai zama tabbatacce. The kawai togiya zai zama haka al'amarin a lokacin da farawa da kuma kawo karshen tsarawa daga wannan vector ne ya daidaita da sifili: a wannan yanayin da kuma ta samfurin da kansa guda zai zama sifili.

Na uku, akwai wani scalar samfurin ne raba, watau da yiwuwar fadada daya daga cikin tsarawa a kan Naira Miliyan Xari biyu dabi'u cewa ba ya kunsa da wani canji a karshe sakamakon da scalar multiplication na vectors. A karshe, a karo na hudu, a cikin multiplication na vectors da wannan real darajar da su scalar samfurin da aka ma ya karu da wannan factor.

A wannan yanayin, idan dukan waɗannan hudu yanayi, za mu iya amince cewa, wannan shi ne wani Euclidean sarari.

Euclidean sarari daga wani m ra'ayi, za a iya halin da wadannan takamaiman misalai:

1. A sauki harka - shi ne samuwar wani sa na vectors tare da wasu daga cikin ka'idojin lissafi, da scalar samfurin.
2. Euclidean sarari an samu a cikin al'amarin, idan ta vectors mu nufin wani guntun sa na real lambobin da aka dabara, ta kwatanta su scalar Naira Miliyan Xari ko samfurin.
3. A musamman idan akwai wani mai Euclidean sarari wajibi ne don gane da abin da ake kira sifili sarari, wanda aka samu a cikin taron cewa tsawon na biyu scalar vectors ne sifili.

Euclidean sarari yana da yawan musamman Properties. Da fari dai, scalar factor iya dauka duka biyu na farko sashi da kuma na biyu factor na scalar samfurin, sakamakon wannan ba zai sha wani canje-canje. Abu na biyu, tare da na farko memba daga rarraba da scalar samfurin, abubuwa da Distributivity biyu kashi. Bugu da kari ga scalar Naira Miliyan Xari vectors, Distributivity yana da wani wuri a cikin hali na subtraction na vectors. A karshe, uku, a scalar multiplication da vector sifili, sakamakon zai zama sifili.

Saboda haka, Euclidean sarari - shi ne mafi muhimmanci geometrical ra'ayi amfani ga warware matsaloli tare da juna tsari na vectors zumunta da juna, domin halaye na wanda irin wannan ra'ayi da aka yi amfani da matsayin ciki samfurin.