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Maja Petrovic

Publications and source records attributed to Maja Petrovic.

9 recordsLinked to original sources
arXiv2024

The area of Hügelschäffer curves via Taylor series

In this paper, we give new Taylor approximative formulae for the area of the egg-shaped parts of Hügelschäffer curves. Based on a parametrization of the Hügelschäffer curve, a formula for the area of the egg-shaped part of such a curve is derived via elliptic integrals of the first and second kind. Furthermore, new approximative formulae for calculating this area derived from standard and double Taylor approximations are given. A representation of the value $\frac{1}π$ was also obtained using an appropriate series.

math.CA↗
arXiv2022

Hugelschaffer egg curve and surface

In this paper we consider Hugelschaffer 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 Hugelschaffer 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 Hugelschaffer model.

math.AG↗
arXiv2019

On the Erdos-Mordell Inequality for Triangles in Taxicab Geometry

In this work the Erdos-Mordell's inequality is examined for the case of a triangle $ABC$ in the taxicab plane geometry. It is shown that the Erdos-Mordell's inequality $R_A + R_B + R_C \, \geq \, w \, (r_a + r_b + r_c)$ holds for triangles with appropriate positions for its points $A$, $B$ and $C$, if $w = 3/2$.

math.MG↗
arXiv2014

On the Extension of the Erdos-Mordell Type Inequalities

We discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.

math.MG↗
arXiv2014

Geometry of some taxicab curves

In this paper we present geometry of some curves in Taxicab metric. All curves of second order and trifocal ellipse in this metric are presented. Area and perimeter of some curves are also defined.

math.HO↗
arXiv2014

The Geometry of Trifocal Curves with Applications in Architecture, Urban and Spatial Planning

In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat's problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms which appear in location problems. We also analyze algebraic equation of these curves and some of their applications in architecture, urbanism and spatial planning. The area and perimeter of trifocal curves are calculated using a Java application. The Java applet is developed for determining numerical value for the Fermat-Torricelli-Weber point and optimal curve with three foci, when starting points are given on an urban map. We also present an application of trifocal curves through the analysis of one specific solution in South Stream gas pipeline project.

math.HO↗