Euclidean makahiki: ka ho'ākāka 'ana, ka waiwai, me na hoailona

ʻO loko o ke kula, i hoʻolauna i ka manaʻo o "Euclidean anahonua", ke kumu nui ai o i i hoʻomōhala puni kekahi mau axioms ka nānā 'ana ma luna o geometric hehee wale e like me kumu, Kekoa, pololei laina ana nā haumāna a pau. A pau o ia pu kuahene mea ua uaʻikeʻia ma ka makahiki "Euclidean ka lewa".

Euclidean wa, i ka wehewehena o ka i ua ma muli o ke kulana o ka scalar multiplication o vectors mea he kūikawā hihia o ka laina (affine) makahiki, a satisfies ka helu o ke koi. Mua, i ka loko huina hoonui o ka vectors ka loa symmetrical, oa ka maʻi lele me ka wahi (m; y me) ma ka hua'ōlelo o ka nui o'ālike i ka maʻi lele me ka wahi (y me; m), akā, e ku pono ana ma ka ao ao.

Ka lua, i loko o ka hanana i i ka scalar huina hoonui o ka maʻi lele me ia iho, i ka hopena o keia hana, e e maikaʻi. Ka mea wale nō koe nae makemake ia i ka hihia i ka wa a ka ho, a pau i hŘnń ia o keia maʻi lele i like ke 'Aʻohe: ma keia hihia a me kona huina hoonui me ia iho, ka mea ia e ia' Aʻohe.

Apana, aia no he scalar huahana mea distributive, oa ka manawa kūpono o ka hoʻonui i kekahi o kona wahi ma luna o ka huina o ka mau loina i e ole entail i kekahi loli ma ka hopena hope loa o ka scalar multiplication o vectors. Eia hoi, ma o ka ha, ma ka multiplication o vectors ma ka ia maoli waiwai o ko lākou scalar huahana ua i mahuahua ma ka hookahi ololi.

Ma ia hihia, ina pau kēia mau eha ana, ua hiki ke paa aku nei au i keia mea he Euclidean pokole.

Euclidean makahiki, mai ka mea hiki wahi o ka hoomaopopo, hiki ke wehewehe aku ma ka kēia ho'ākāka examples:

1. Na simplest hihia - o ka loaʻa nui o ka lākou o nā vectors me kekahi o nā kumu o ke kanawai o ka anahonua, ka scalar huahana.
2. Euclidean makahiki ua loaa i loko o ka hihia, ina e vectors mākou makemake i kekahi finite lākou o maoli helu me ka haawiia mai haʻilula, hōʻike no lākou scalar huina a huahana.
3. A kūikawā hihia o ka Euclidean pokole mea pono e ike i ka ai-i kapaia o 'Aʻohe makahiki, a ua loaa i loko o ka hanana i ka lōʻihi o nā scalar vectors mea Aʻohe.

Euclidean makahiki i ka helu ana o kekahi waiwai. Mua, scalar ololi hiki e lawe no nā ka māhele mua a me ka lua o ka ololi o ka scalar huina hoonui, i ka hopena o keia, e undergo kekahi hoʻololi. Ka lua, a ka lala mua, mai ka puunaue ana o ka scalar huina hoonui, hana a Distributivity lua hehee ai. Ma waho aʻeo i ka scalar huina o vectors, Distributivity ua loaa he wahi i loko o ka hihia o ka subtraction o vectors. Eia hoi, ke kolu, ma scalar multiplication o ka maʻi lele i Aʻohe, i ka hopena, e hoi e Aʻohe.

Pela, ke Euclidean wa - o ka mea nui geometrical manaʻo hoʻohana no ka hoʻoponopono pilikia me ka manao lokahi hoʻoponoponoʻana o Kamehameha o vectors pili i kekahi i kekahi, no na ano o i ia manaʻo ua hoʻohana 'ia e like me ka pā huahana.