Applicable Analysis and Discrete Mathematics 2023 Volume 17, Issue 1, Pages: 179-196
https://doi.org/10.2298/AADM220526027P
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Hügelschäffer egg curve and surface

Petrović Maja ORCID iD icon (University of Belgrade, The Faculty of Transport and Traffic Engineering, Belgrade, Serbia), majapet@sf.bg.ac.rs
Malešević Branko ORCID iD icon (University of Belgrade, School of Electrical Engineering, Belgrade, Serbia), branko.malesevic@etf.bg.ac.rs

In this paper we consider Hügelschäffer cubic curves which are generated using appropriate geometric constructions. The main result of this work is the mode of explicitly calculating the area of the egg-shaped part of the cubic curve using elliptic integrals. In this paper, we also analyze the Hügelschäffer surface of cubic curves for which we provide new forms of formulae for the volume and surface area of the egg-shaped part. Curves and surfaces of ovoid shape have wide applicability in aero-engineering and construction, and are also of biologic importance. With respect to this, in the final section, we consider some examples of the real applicability of this Hügelschäffer model.

Keywords: Egg shaped curve/surface, Hügelschäffer’s model, Elliptic integral

Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 451-03-68/2022-14/200103

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