Yıl 2018,
Cilt: 7 Sayı: 2, 48 - 53, 31.12.2018
Mustafa Altın
,
Müge Karadağ
Kaynakça
- 1. Hanbay K, Alpaslan N, Talu MF, Hanbay D. Principal curvatures based rotation invariant algorithms for efficient texture classification. Neurocomputing [Internet]. 2016;199:77–89. Available from: http://www.sciencedirect.com/science/article/pii/S0925231216300522
- 2. Beyer WH. Standard Mathematical Tables. Boca Raton: FL: CRC Press; 1987. 216 p.
- 3. Gray A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton: FL: CRC Press; 1997. 50-52 p. 4. Lawrence JD. A Catalog of Special Plane Curves. New York: Dover Publications Inc.; 1972. 192-197 p.
- 5. Lockwood EH. “The Cycloid.” Ch. 9. In: A Book of Curves. Cambridge, England: Cambridge University Press; 1967. p. 80–9.
- 6. MacTutor History of Mathematics Archive [Internet]. Available from: http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cycloid.html
- 7. Smith DE. Special Topics of Elementary Mathematics. In: History of Mathematics, Vol 2. New York: Dover Publications Inc.; 1958. p. 327.
- 8. Wells D. The Penguin Dictionary of Curious and Interesting Geometry. Londra: Penguin; 1991. 44-47 p.
- 9. Yates RC. Cycloid. In: A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards; 1952. p. 65–70.
- 10. E. Ethemoglu. E^n deki Kendine Benzer Yüzeylerin Bir Karekterizasyonu. Uludağ Üniversitesi; 2013.
- 11. Etemoglu E, Arslan K, Bulca B. Self similar surfaces in Euclidean space. Selcuk J Appl Math,. 2013;14(1):71–81.
- 12. Anciaux H. Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in Cn. Geom Dedicata [Internet]. 2006;120(1):37–48. Available from: http://link.springer.com/10.1007/s10711-006-9082-z
- 13. Uribe-Vargas R. On Vertices, focal curvatures and differential geometry of space curves. Bull Brazilian Math Soc. 2005;36(3):285–307.
- 14. Hacısalihoğlu HH. Differensiyel Geometri. Ankara: Gazi Üniversitesi Basın Yayın Yüksekokulu Basımevi; 1983. 1-895 p.
- 15. Encheva RP, Georgiev GH. Similar Frenet curves. Results Math. 2009;55(3):359–72.
Kendine Benzer Eğri Olmayan Bazı Özel Eğriler
Yıl 2018,
Cilt: 7 Sayı: 2, 48 - 53, 31.12.2018
Mustafa Altın
,
Müge Karadağ
Öz
Görüntü işleme
ve örüntü tanıma uygulamalarında yer bulan kendine benzer eğriler bir çok
araştırmacı tarafından çalışılmıştır. Bu çalışmada Öklid uzayında Kardioid ,
Saykloid, Limaçon, Astroid, Eş açılı spiral eğrilerinin kendine benzer eğri
olup olmadıkları incelenmiştir. Ayrıca bu eğrilerin kendine benzer eğri
olmaması için gerekli şartlar elde edilmiştir.
Kaynakça
- 1. Hanbay K, Alpaslan N, Talu MF, Hanbay D. Principal curvatures based rotation invariant algorithms for efficient texture classification. Neurocomputing [Internet]. 2016;199:77–89. Available from: http://www.sciencedirect.com/science/article/pii/S0925231216300522
- 2. Beyer WH. Standard Mathematical Tables. Boca Raton: FL: CRC Press; 1987. 216 p.
- 3. Gray A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton: FL: CRC Press; 1997. 50-52 p. 4. Lawrence JD. A Catalog of Special Plane Curves. New York: Dover Publications Inc.; 1972. 192-197 p.
- 5. Lockwood EH. “The Cycloid.” Ch. 9. In: A Book of Curves. Cambridge, England: Cambridge University Press; 1967. p. 80–9.
- 6. MacTutor History of Mathematics Archive [Internet]. Available from: http://www-groups.dcs.st-and.ac.uk/~history/Curves/Cycloid.html
- 7. Smith DE. Special Topics of Elementary Mathematics. In: History of Mathematics, Vol 2. New York: Dover Publications Inc.; 1958. p. 327.
- 8. Wells D. The Penguin Dictionary of Curious and Interesting Geometry. Londra: Penguin; 1991. 44-47 p.
- 9. Yates RC. Cycloid. In: A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards; 1952. p. 65–70.
- 10. E. Ethemoglu. E^n deki Kendine Benzer Yüzeylerin Bir Karekterizasyonu. Uludağ Üniversitesi; 2013.
- 11. Etemoglu E, Arslan K, Bulca B. Self similar surfaces in Euclidean space. Selcuk J Appl Math,. 2013;14(1):71–81.
- 12. Anciaux H. Construction of Lagrangian Self-similar Solutions to the Mean Curvature Flow in Cn. Geom Dedicata [Internet]. 2006;120(1):37–48. Available from: http://link.springer.com/10.1007/s10711-006-9082-z
- 13. Uribe-Vargas R. On Vertices, focal curvatures and differential geometry of space curves. Bull Brazilian Math Soc. 2005;36(3):285–307.
- 14. Hacısalihoğlu HH. Differensiyel Geometri. Ankara: Gazi Üniversitesi Basın Yayın Yüksekokulu Basımevi; 1983. 1-895 p.
- 15. Encheva RP, Georgiev GH. Similar Frenet curves. Results Math. 2009;55(3):359–72.