Nzira yekuwana nayo kure mu ndege yekuranganidza

Mune mathematics, zvose algebra uye geometry zvinogadzirisa mabasa kuti awane kure nekusvika pane imwe kana mutsara wakarurama kubva pane chimwe chinhu chakapiwa. Icho chiri munzira dzakasiyana zvakasiyana, kusarudzwa kwaro kunobva pane dambudziko rekutanga. Funga kuti ungawana sei nzvimbo iri pakati pezvinhu zvakapiwa mumamiriro akasiyana.

Kushandisa zviyero zvokuyera

Pachikoro chekutanga chekuongorora masvomhu yesayenzi, vanodzidzisa nzira yekushandisa zvidzidzo zvekutanga (zvakadai somutongi, protractor, kambasi, katatu uye nevamwe). Tsvaga muganhu pakati pemakona kana mitsetse nerubatsiro rwavo hauna kuoma. Zvakakwana kuisa chikwata chemazana uye kunyora mhinduro yacho. Izvo zvakakosha kuziva kuti kureba kuchave kwakaenzana nekureba kwemutsara wakarurama, iyo inogona kutorwa pakati pepakati, uye munyaya yemirairo yakafanana - iyo inofananidzwa pakati pavo.

Kushandiswa kwemaoremusi uye marwadzo ejometri

Muchikoro chepamusoro dzidza kuyera nzvimbo yacho pasina rubatsiro rwezvinhu zvakakosha kana mapepa. Nokuda kweizvi, tinoda maoremori akawanda, axioms, uye uchapupu hwavo. Kazhinji matambudziko ekuti ungawana sei nzvimbo yacho yakaderedzwa kusvika pakuumbwa kwekona katatu uye kutsvaga kwaro. Kugadzirisa matambudziko akadaro zvakakwana kuziva dzidziso yePythagorean, iyo yezvinhu zvitatu, uye nzira dzekuchinja kwavo.

Points on the coordinate plane

Kana pane nharo mbiri uye nzvimbo yavo yakagadzirirwa ku-coordinate axis, sei kuwana nzvimbo kubva kune imwe kuenda kune imwe? Mhinduro yacho inosanganisira zvikamu zvakasiyana-siyana:

1. Tinobatanidza mapepa emutsara wakarurama, kureba kwayo kuchava kure kure pakati pavo.
2. Tinoona musiyano muhutano hwehutano hwemashoko (k; p) ega ega ega: | k ₁ - k ₂ | = d ₁ uye | p ₁ - p ₂ | = d ₂ (tinotora hutsika modulo, sezvo kureba hakugoni kuipa) .
3. Mushure meizvi, tinovaka nhamba dzinoguma muzvikwereti uye tinowana mubare wavo: d ₁ ² + d ₂ ²
4. Nhanho yekupedzisira ndiyo kubviswa kwepakati pekona yenhamba inoguma. Iyi ichange iri kure pakati pezvikamu: q = V (d ₁ ² + d ₂ ² ).

Somugumisiro, sarudzo yose inogadzirwa neshoko rimwe chete, uko kureba kwakaenzana neyero miviri yehuwandu hwezvikwata zvehutano hwakasiyana:

D = V (| k ₁ - k ₂ | ² + | p ₁ - p ₂ | ² )

Kana pane mubvunzo pamusoro pokuti ungawana sei nzvimbo kubva kune imwe nzvimbo kuenda kune imwe mumatatu-dimensional space, kutsvaga mhinduro kune iyo hakuzove kwakasiyana zvikuru neyo yakapiwa pamusoro. Mhinduro yacho inoshandiswa uchishandiswa nenzira inotevera:

Q = V (| k ₁ - k ₂ | ² + | p ₁ - p ₂ | ² + | e ₁ - e ₂ | ² )

Parallel straight lines

Izvo zvinongororwa zvichibva kune imwe nzvimbo inenge iri pane imwe mutsara kusvika kune yakafanana, uye iri kure. Pakugadzirisa matambudziko mundiza, zvakakosha kuwana hurumende dzechinangwa chipi zvacho cheimwe yemitsara. Uye woverenga kureba kubva pairi kusvika kune yechipiri mutsara wakarurama. Nokuda kweizvi, tinovaderedza kusvika kuongorori yakawanda yemutsara wakarurama we fomu Ax + Bx + C = 0. Iyo inozivikanwa kubva kune imwe nzvimbo yemigwagwa yakafanana iyo coefficients yavo A uye B ichave yakaenzana. Muchiitiko ichi, nzvimbo iri pakati pemitsetse yakafanana inogona kuwanikwa neyamuyo:

D = | C ₁ - C ₂ | / V (A ² + B ² )

Nokudaro, paunopindura mubvunzo wekuti ungawana sei nzvimbo kubva pane chimwe chinhu chawakapiwa, zvakakosha kutungamirirwa nemamiriro ezvinhu ezvo basa uye zvishandiso zvinopiwa kuti zvigadzirise. Zvinogona kuva zvose maitiro ekuyera, uye maoreoremu nemaitiro.