Danga Euclidean: tanthauzo, katundu, zizindikiro

Ngakhale mu sukulu, ophunzira onse tikuuzidwa kuti maganizo "Euclidean Masamu", chakudya chachikulu chimene kwambiri za padziko axioms ochepa zochokera zinthu zojambula monga mfundo ndege, molunjika mzere kuyenda. Onse pamodzi kupanga zimene kale ndi mawu akuti "Euclidean danga".

Euclidean danga, tanthauzo la zomwe zachokera udindo wa chulutsa scalar wa zamoyo zina imakhala nkhani yapadera ya liniya (affine) danga, zomwe imakwaniritsa zingapo zofunika. Choyamba, mankhwala lamkati la zamoyo zina ndi symmetrical mwamtheradi, mwachitsanzo vekitala ndi ndondomeko (×; Y) mwa mawu a kuchuluka ndi zofanana kwa vekitala ndi ndondomeko (Y; x), koma zosiyana mu dera.

Kachiwiri, kukachitika kuti anapanga mankhwala scalar wa vekitala ndi lokha chifukwa cha zimenezi adzakhala positive. Yekha adzakhala choncho pamene poyambira ndi kutha ndondomeko ya vekitala ichi ndi wofanana ndi ziro: Pankhaniyi ndi mankhwala ake ndi chokha womwewo udzakhala ziro.

Chachitatu, pali mankhwala scalar ndi distributive, mwachitsanzo kuthekera kuwonjezera amodzi kwa ndondomeko ake pa ndalama makhalidwe awiri amene si zikuphatikizapo kusintha zotsatira zake zomalizira za chulutsa scalar wa zamoyo zina. Pomalizira pake, chachinayi, chulutsa zamoyo zina ndi chimodzimodzi phindu lenileni la mankhwala awo scalar amadziwikanso chinawonjezeka ndi chinthu chomwecho.

Zikatero, ngati zinthu izi zonse zinayi, tikhoza kunena motsimikiza kuti izi ndi danga Euclidean.

danga Euclidean ku mfundo maganizo, akhoza yodziwika ndi zitsanzo zotsatirazi chindunji:

1. Nkhani losavuta - ndi kupezeka kwa m'ndandanda wa zamoyo zina ndi zina malamulo zofunika masamu, mankhwala scalar.
2. danga Euclidean analandira mu mulanduwo, ngati ndi zamoyo zina tikutanthauza ena amalire ya manambala weniweni ndi chilinganizo anapatsidwa ananena scalar awo ndalama kapena mankhwala.
3. Nkhani wapadera wa danga Euclidean m'pofunika kuzindikira otchedwa ziro danga, amene analandira kukachitika kuti kutalika kwa zamoyo zina zonse scalar ndi ziro.

danga Euclidean angapo katundu yeniyeni. Choyamba, scalar chinachititsa kumwedwa kwa onse bulaketi woyamba ndi chinthu chachiwiri cha mankhwala scalar chifukwa cha si zimasintha iliyonse. Kachiwiri, pamodzi woyamba kuchokera kameredwe mankhwala scalar, amachita ndi Distributivity chinthu chachiwiri. Kuwonjezera ndalama scalar wa zamoyo zina, Distributivity ali ndi malo zinachitikira wochotsera wa zamoyo zina. Pomaliza, achitatu, mu scalar chulutsa wa vekitala kuti ziro, chifukwa kudzakhala ziro.

Choncho, danga Euclidean - ndi zofunika kwambiri geometrical lingaliro ntchito pothetsa mavuto ndi makonzedwe tonse zamoyo zina wachibale wina ndi mzake, chifukwa makhalidwe amene lingaliro loterolo ntchito ngati mankhwala lamkati.