La siman in ay diyaarad ku saabsan: xaalad iyo hantida

Barbaro ah in ay diyaaradda waa fikrad marka hore u muuqday in joomateri ee Euclidean in ka badan laba kun oo sano ka hor.

astaamaha ugu muhiimsan ee geometry classical

dhalashada anshaxa sayniska this la xidhiidha shuqullada caanka ah ee Faylasuuf Giriigga ee hore Euclid, kuwaas oo ku qoray BC saddexaad qarnigii, ee "Qaybaha" buugga. Kala qaybiyaa saddex iyo toban buugaagta, "Qaybaha" waa guul ugu sareeya ee dhammaan xisaabta qadiimiga ah iyo fasiray geliyey mabaa'diida aasaasiga la xiriira sifooyinka tirooyinka diyaarad.

xaalad Qadiimiga ah ee diyaaradaha isku midka ah waxaa la diyaariyey sida soo socota: laba diyaaradood waxaa loo yeedhi karaa isku midka ah haddii kasta oo ay leeyihiin ma dhibcood caadi ah. Tani waxay ka akhrisan Euclidean shaqada postulate shanaad.

Guryaha diyaarado isku midka ah

joomatariga The Euclidean ee go'doonka ah, caadi ahaan shan:

• hantida waa hore oo kale (oo u tilmaamaya isku midka ah in ay diyaarad ay la aqonsado). Iyada oo hal dhibic kaliya, oo ku taala meel ka baxsan diyaarad gaar, aan sawiri kartaa mid ka mid ah oo kaliya hal diyaarad isku midka ah

• hantida labaad (sidoo kale loo yaqaan guryaha triplicate). In kiiska halkaas oo laba diyaaradood waa isku midka ah marka la eego saddexaad, dhexdooda, ay sidoo kale la sinnaan.

• hantida Saddexaad (si kale loo dhigo, waxa la yidhaahdaa waa line a hantida intersecting isku midka ah in ay diyaaradda). Haddii qaaday line si gooni gooni ah si toos ah gudbo mid ka mid ah diyaaradaha isku midka ah, waxay u gudbi doonaa oo kale.

• hantida afaraad (hantida khadadka toosan xardhay on diyaaradaha siman midba midka kale). Marka laba diyaaradood isku midka midaysan saddexaad (xagal kasta), oo ay line of isgoyska isagoo isku midka ah

• hantida Shanaad (hantida oo qeexaya qaybaha kala duwan ee khadadka si toos ah isku midka ah, taas oo ah been u dhexeeya diyaaradaha siman midba midka kale). The qaybo ka mid ah khadadka isku midka ah, kuwaas oo ku lifaaqan oo u dhexeeya laba diyaaradood isku midka ah daruuri siman.

Barbaro ah in ay diyaarada ee non-Euclidean geometry

hab noocan ah waa in si gaar ah joomateri ee Lobachevsky iyo Riemann. Haddii Euclidean geometry waxaa fuliyey on Toostaan guri, ka dibna Lobachevsky meelaha xun qalooca (geesba fudud ku riday), halka Riemann helo ay xaqiijinta in meelaha wanaagsan qalooca (si kale loo dhigo - goobaha). Waxaa jira aragti aad caadi u soocayo in Lobachevsky isku midka ah in ay diyaaradda (iyo sidoo kale line) jareyso. Si kastaba ha ahaatee, taasi run ma aha. Indeed dhalashada geometry hyperbolic ayaa lala xiriiriyay wax caddeeya in postulate shanaad Euclid iyo beddelo views it on, laakiin qeexidda aad diyaarado isku midka ah iyo khadadka toos ah oo macnaheedu yahay in aanay waxba u gudbi karin Lobachevsky mana Riemann, in wax kasta oo goobaha ay la fuliyo. Isbeddel qalbiga iyo ereyada waa sida soo socota. In meel of postulate in diyaarad isku midka ah mid ka mid ah oo kaliya waxaa loo qeybin karaa iyada oo dhibic ma on diyaarad siiyey, yimid dejinta kale, iyada oo loo marayo hal dhibic in been ma diyaarad gaar qaadan kartaa laba, ugu yaraan, si toos ah, kuwaas oo ku jira mid ka mid ah diyaarad la this iyo ha u gudbaan.