ANALYSIS OF GEODESICS ON DIFFERENT SURFACES

  • Miroslav Maksimović Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica, Serbia
  • Tanja Jovanović Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica, Serbia
  • Eugen Ljajko Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica, Serbia
  • Milica Ivanović Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica, Serbia
DOI: https://doi.org/10.5937/univtho10-20589
Keywords: Geodesics, u- and v- parameter curve, Developable surface, Minimal surface

Abstract


It is widely known that some surfaces contain special curves as a geodesics, while a lots of geodesics on surface have complicated shapes. Goal of this research is to find on what surfaces are u- and v- parameter curves geodesics. Developable surfaces that contain a given plane curve as a geodesic are studied in the article, whereas the plane curve is also an initial u-parameter curve on that surface. Parametric equations of the minimal surfaces that contain an epicycloid as a geodesic are also given. Visualization of geodesics was done in  Mathematica.

References

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Published
2020/06/30
Issue
Vol. 10 No. 1 (2020)
Section
Original Scientific Paper

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