3-boyutlu Öklid uzayında Conchoid eğri ve yüzeyleri

Yıl 2018, Cilt: 20 Sayı: 2, 467 - 481, 01.12.2018

Betül Bulca S. Neslihan Oruç Kadri Arslan

https://doi.org/10.25092/baunfbed.485640

Cited By: 1

Öz

Bu çalışmada ilk olarak düzlemde conchoid eğrileri çalışılmıştır. Conchoid eğrisinin eğriliği hesaplanıp bazı sonuçlar verilmiştir. Ayrıca 3-boyutlu Öklid uzayında conchoid eğrisiyle elde edilen dönel yüzeyler ele alınmıştır. Bu yüzeylerin Gauss ve ortalama eğrilikleri hesaplanmış, bunlarla ilgili örnekler verilip grafikleri çizdirilmiştir. Son olarak 3-boyutlu Öklid uzayında conchoidal yüzeyler üzerinde durulmuş ve conchoidal yüzeylerin flat ve minimal olma şartlarına bakılmıştır. Conchoidal yüzey örnekleri de verilip grafikleri çizdirilmiştir.

Anahtar Kelimeler

Conchoid, Pascal Limaçonu, Gauss eğrilik, ortalama eğrilik

Conchoid curves and surfaces in Euclidean 3-Space

Öz

In this study firstly, we study with conchoid curves in Euclidean plane E2. We calculate the curvature of the conchoid curve and give some results. Furthermore, we consider the surface of revolution given with the conchoid curve in Euclidean 3-space E3. The Gaussian and mean curvature is calculated of these surfaces. Also we give some examples and plot their graphics. Finally we study conchoidal surface in Euclidean 3-space. We give some results for the conchoidal surface to become flat and minimal. We give an example and plot the garphics of the conchoidal surfaces.

Anahtar Kelimeler

Conchoid, Limaçons Pascal, Gaussian curvature, mean curvature

Kaynakça

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