Euclidean ohere: definition, Njirimara, ịrịba ama

Ọbụna akwụkwọ, ụmụ akwụkwọ nile na-ẹkenam ka echiche nke "Euclidean jiometrị", isi oriri nke na-elekwasị anya gburugburu a ole na ole axioms dabeere na geometric ọcha dị ka ihe, ụgbọ elu, ogologo akara ije. All nke ha ọnụ na-etolite ihe a na-ama mara site na okwu ahụ bụ "Euclidean ohere".

Euclidean ohere, na definition nke nke dabeere ọnọdụ nke scalar multiplication nke Vektọ bụ a pụrụ iche banyere linear (affine) ohere, nke na-eme a ọnụ ọgụgụ nke chọrọ. Firstly, n'ime ngwaahịa nke Vektọ bụ nnọọ symmetrical, ie ndị vector na-achịkọta (x; y) na okwu nke ukwu bụ yiri ka vector na-achịkọta (y; x), ma abụghị na direction.

Nke abuo, na ihe omume nke mere scalar ngwaahịa nke vector na onwe ya, na N'ihi ihe a ga-nti. The naanị wezụga ga ịbụ ikpe mgbe amalite na-agwụcha na-achịkọta ndị a vector bụ hà efu: na nke a na ya ngwaahịa na ya onwe ya otu ga-efu.

Nke atọ, e nwere a scalar ngwaahịa bụ distributive, ie ekwe omume nke ịgbasa onye nke ya na-achịkọta na nchikota nke abụọ ụkpụrụ na-adịghị abuana mgbanwe ọ bụla na ikpeazụ na n'ihi nke scalar multiplication nke Vektọ. N'ikpeazụ, na nke-anọ, na multiplication nke Vektọ site n'otu bara ezigbo uru nke ha scalar ngwaahịa na-amụba site otu ihe na-akpata.

Na ikpe, ma ọ bụrụ na niile anọ ndị a na ọnọdụ, anyị nwere ike n'enweghị ekwu na nke a bụ a Euclidean ohere.

Euclidean ohere si a bara uru echiche, nwere ike ji na-esonụ kpọmkwem ihe atụ:

1. The mfe ikpe - bụ nnweta a set of Vektọ na ihe ụfọdụ dị mkpa iwu nke jiometrị, na scalar ngwaahịa.
2. Euclidean ohere a nwetara na ikpe, ma ọ bụrụ na site Vektọ anyị pụtara a ụfọdụ nwere oke set nke ezigbo nọmba na a nyere usoro, na-akọwa ha scalar nchikota ma ọ bụ ngwaahịa.
3. A pụrụ iche bụrụ na nke a Euclidean ohere dị mkpa iji na-aghọta ihe a na-akpọ efu ohere, nke na-enwetara na ihe omume ahụ na ogologo nke ma scalar Vektọ bụ efu.

Euclidean ohere nwere ọtụtụ kpọmkwem Njirimara. Firstly, scalar akpata nwere ike a n'ihi ma mbụ mgbodo na nke abụọ na-akpata nke scalar ngwaahịa, n'ihi nke a ga-ata ọ bụla mgbanwe. Nke abuo, tinyere ndị mbụ so si nkesa nke scalar ngwaahịa, na-eme na Distributivity abụọ mmewere. Na mgbakwunye na scalar nchikota nke Vektọ, Distributivity nwere ebe na ikpe nke mwepu nke Vektọ. N'ikpeazụ, thirdly, na scalar multiplication nke vector na efu, n'ihi ga-efu.

N'ihi ya, Euclidean ohere - bụ ihe kasị mkpa geometrical echiche na-eji maka idozi nsogbu na ibe ndokwa nke Vektọ ikwu onye ọ bụla ọzọ, n'ihi na e ji mara nke ndị dị otú ahụ echiche na-eji dị n'ime ngwaahịa.