Fokalne plohe

Šokčić, Ivo (2015) Fokalne plohe. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

The focal set of a surface is the locus of points of its centres of curvature. Generally, a (regular) focal set of surface may consist of two surfaces, so called focal surfaces or evolutes, then of one surface and one curve, or of two curves. In this thesis, differentialgeometric properties of the focal set are studied. In the special case, when the focal set consists of a surface and a curve, so called canal surfaces are defined. Also, their special classes are analysed: tubes and rotation surfaces. Finally, in the case when the focal set consists of two curve, we defined cyclides of Dupin of elliptic-hyperbolic type. They are named after the French mathematician Charles Dupin who studied them in the 19th century. This thesis presents all the definitions related to the focal set of a surface. All theoretical material is accompanied by concrete examples and figures made using the software package "Wolfram Mathematica" [7].

Item Type: Thesis (Diploma thesis)
Keywords: focal surfaces, canal surfaces, cyclides of Dupin
Supervisor: Milin-Šipuš, Željka
Date: 2015
Number of Pages: 49
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 28 Oct 2015 11:54
Last Modified: 28 Oct 2015 11:54
URI: http://digre.pmf.unizg.hr/id/eprint/4192

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