Paralel

Başlığın diğer anlamları için paralel (anlam ayrımı) sayfasına bakınız.
a ve l doğruları arasındaki uzaklık (r) doğrular boyunca aynıdır.

Paralel veya koşut[1], uzunluğu boyunca birbirinden eşit uzaklıkta bulunan doğru ya da düzlemlerin birbirlerine göre durumlarını tanımlamakta kullanılan bir sıfat.[2] Parallellik Öklid evreninde mümkündür ve Öklid'in paralel aksiyomunun temelini oluşturur.

Matematikte paralellik sembolü ile ifade edilir. Örneğin ifadesi "AB doğrusu ile CD doğrusu paraleldir," anlamına gelir.

Paralel aksiyomu

Paralel aksiyomuna göre iki doğru ile bunları kesen üçüncü bir doğru arasındaki iç açıların toplamı (α+β) 180° den küçükse, bu doğrular açıların bulunduğu tarafta yeterli kadar uzatıldıklarında mutlaka kesişirler.

Paralel aksiyomu ya da paralel postülası, Öklidci geometriyi oluşturan 5 aksiyomdan birisidir. Bu aksiyoma göre bir düzlemdeki herhangi bir doğru üzerinde bulunmayan bir noktadan, o doğruya paralel sadece bir doğru çizilebilir.[3] Öklid'in diğer aksiyomlarının aksine kendinden ispatlı[4] değildir.[3] 19. yüzyılda Nikolay Lobachevsky ve János Bolyai'nin (1802–60) birbirlerinden bağımsız olarak paralel aksiyomu değiştirmeleri, tamamen kararlı olan Öklidci olmayan geometrinin ortaya çıkmasını sağlamıştır.[3]

Kaynakça

  1. ^ "TDK Güncel Türkçe Sözlük". 29 Aralık 2018 tarihinde kaynağından arşivlendi. Erişim tarihi: 30 Ocak 2024. 
  2. ^ "parallel." Oxford Dictionary of English 2e, Oxford University Press, 2003.
  3. ^ a b c "parallel postulate." Encyclopædia Britannica Ultimate Reference Suite. Chicago: Encyclopædia Britannica, 2011.
  4. ^ self-evident Ç.N.

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