Layi daya da jirgin saman: yanayin da kaddarorin

Layi daya da jirgin saman shi ne ra'ayi na farko ya bayyana a cikin Euclidean lissafi don fiye da shekara dubu biyu da suka wuce.

Main halaye na gargajiya lissafi

Haihuwar wannan kimiyya horo hade da shahararrun ayyukan tsoho Greek Falsafa Euclid, wanda ya rubuta a cikin na uku karni BC, ƙasida "Abubuwa". Kasu kashi goma sha uku littattafai, "Abubuwa" shi ne babban rabo mai girma daga duk tsoho lissafi da kuma bayyana da muhimman hakkokin tenets hade da kaddarorin jirgin Figures.

Gargajiya yanayin layi daya jirage da aka tsara kamar haka: biyu jirage iya kira a layi daya, idan sun kowanne da babu kowa da maki. Wannan karanta Euclidean biyar hakan aiki.

Properties na layi daya jirage

A Euclidean lissafi na zama ruwan dare, yawanci biyar:

• A dukiya ne na farko (kuma layi daya da jirgin saman ya bayyana su bambancinsa). Ta hanyar wata guda aya, wanda ya ta'allaka a waje na wannan jirgi musamman, za mu iya zana daya da daya kawai a layi daya jirgin sama

• Na biyu dukiya (kuma aka sani da kaddarorin triplicate). A cikin akwati inda biyu jirage ne a layi daya tare da girmamawa ga na uku, tsakanin kansu, suna kuma a layi daya.

• Na uku dukiya (a cikin wasu kalmomi, shi ne ake kira da dukiya line intersecting layi daya da jirgin saman). Idan dauki dabam mike layin crosses daya daga wadannan layi daya jirage, shi zai haye da wani.

• Fourth dukiya (dũkiyõyin madaidaiciya Lines sassaka a kan jirage a layi daya to juna). Lokacin da biyu a layi daya jirage rarraba da uku (daga duk wani kwana), kuma su line na rarrabawa kasancewa a layi daya

• Biyar dukiya (da dukiya da bayyana daban-daban segments na layi daya madaidaiciya Lines, wanda karya tsakanin jirage a layi daya to juna). A segments na layi daya Lines, wanda aka kewaye tsakanin biyu a layi daya jirage dole daidai.

Layi daya da jirgin saman a ba Euclidean lissafi

Irin wannan dabarar ne musamman da lissafi na Lobachevsky da Riemann. Idan Euclidean lissafi aka aiwatar a kan lebur sarari, sa'an nan Lobachevsky a barnatar mai lankwasa sarari (mai lankwasa kawai ya sa), yayin da Riemann shi sami ta ganin a gaskiya ma mai lankwasa sarari (a cikin wasu kalmomi - yankunan). Akwai matukar kowa stereotypical ra'ayin cewa Lobachevsky layi daya da jirgin saman (da ma line) rarraba. Duk da haka, wannan ba gaskiya ba ne. Lalle haihuwar hyperbolic lissafi aka hade da wani hujja na Euclid ta biyar da hakan da kuma canza ra'ayi kan shi, amma sosai definition na layi daya jirage da kuma madaidaiciya Lines yana nufin cewa ba za su iya haye kuma Lobachevsky kuma Riemann, a duk abin da sarari suna aiwatar. A canji na zuciya da kuma wording ne kamar haka. A wurin da hakan da cewa daya kawai a layi daya jirgin sama za a iya kõma ta nufi ba a kan wani ba jirgin sama, ya zo da wani halitta: ta hanyar wani batu da cewa ba ya kwanta a wannan jirgi musamman iya daukar biyu, a kalla, a mike, wanda yake a cikin daya jirgin sama tare da wannan, kuma kada ku ƙetare shi.