Akaererana ndege: mamiriro uye zvivako

Parallel kuti ndege ndiyo pfungwa yokutanga akazviratidza Euclidean geometry kuti anopfuura zviuru zviviri apfuura.

Unhu Zvikuru dzekare geometry

Kuberekwa chirango ichi dzesayenzi chokuita nemabasa akakurumbira vekare wechiGiriki ainzi Euclid, uyo akanyora wechitatu BC, turakiti racho "Zvinoumba" remakore. Rakakamurwa mabhuku gumi nenhatu, "Elements" ndiyo inonyanya kubudirira vose masvomhu zvekare uye vakatsanangura dzinokosha zvinodavirwa muchitendero chokuita ehupfumi ose ndege nemifananidzo.

akanga Classical mamiriro inofambirana ndege akagadzira sezvinotevera: ndege mbiri anganzi zvakafanana kana ivo mumwe havana zvakafanana pfungwa. Izvi verenga Euclidean cheshanu uchapupu basa.

Properties ose inofambirana ndege

The Euclidean geometry pamusoro kure, kazhinji shanu:

• The pfuma ndiyo yokutanga (uye akaererana ndege anorondedzera zvavo yokusiyana). Kuburikidza chete pfungwa, riri kunze zvikuru ndege iyi, tinogona kuswedera mumwe uye imwe chete yakafanana ndege

• The pfuma wechipiri (aizivikanwawo ehupfumi triplicate). In Kana apo ndege mbiri zvinofanana noruremekedzo rechitatu, pakati pachavo, vari zvakare kuenderana.

• The pfuma ndiyo yechitatu (nemamwe mashoko, inonzi pfuma mutsetse intersecting akaererana ndege). Kana ikatorwa yoga yakarurama mutsetse michinjikwa mumwe yakafanana ndege izvi, zvichava kuyambuka uye mumwe.

• pfuma chechina (pfuma kururamisa mitsetse zvokutemerwa ndege kuenderana mumwe). Apo vaviri dzakafanana ndege piringisha yechitatu (chero necheparutivi), uye avo aitevedzana mharadzano kuva yakafanana

• Wechishanu pfuma (chepfuma chinorondedzera zvikamu zvakasiyana-siyana yakafanana kururamisa mitsetse, izvo nhema pakati ndege kuenderana nomumwe). The mapazi eumambo dzakafanana mitsetse, izvo akanyudzwa pakati maviri nepadivi ndege hazvo zvakaenzana.

Parallel kuti ndege vasiri Euclidean geometry

Akadaro nzira iri kunyanya geometry pamusoro Lobachevsky uye Riemann. Kana Euclidean geometry iri rakatangwa pamusoro sandara dzezvimwe, ipapo Lobachevsky mu isakarurama curved dzezvimwe (curved nyore), ukuwo Riemann unosvikowana Kuziva raro chokwadi curved dzezvimwe (nemamwe mazwi - nzvimbo). Pane vakawanda stereotypical maonero kuti Lobachevsky akaererana ndege (uyewo mutsetse) piringisha. Zvisinei, ichi hachisi chokwadi. Zvechokwadi kuberekwa hyperbolic geometry aishamwaridzana uchapupu Euclid kuti wechishanu uchapupu uye kuchinja maonero pamusoro payo, asi chaizvo tsanangudzo inofambirana ndege uye yakarurama mitsetse kunoreva kuti havagoni kuyambuka kana Lobachevsky kana Riemann, mune chero dzezvimwe zvavari rakatangwa. Kuchinja mwoyo uye mashoko ari sezvinotevera. Panzvimbo uchapupu kuti kufanana ndege imwe chete inogona kuwanikwa kuburikidza pfungwa kwete pamusoro kupiwa mundege, akauya mumwe Pfungwa: kuburikidza pfungwa kuti hahuwanikwi kufambidzana ndege iyi inogona kutora vaviri, zvinenge, kururamisa, vari imwe ndege iyi uye regai kuyambuka naro.