Maja Petrovic

Visualization of Weber's curves and surfaces with applications in some optimization problems

In this paper, we present a Java application for visualization of Webers curves and surfaces generated by at most 3 foci, directrix lines or planes.

A computer verification of a conjecture about the Erdös-Mordell curve

In this paper we consider Erdös-Mordell inequality and its extension in the plane of triangle to the Erdös-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one conjecture that relates to Erdös-Mordell curve.

Directorial Surfaces and Potential Applications in Cupola Design

Architecture, being an inexhaustible source of ideas for shaping both interior and exterior, is in high demand of the development of novel methods for geometric form generation. Nowadays the architectural objects, in regard to high degree of computer design and material technology development, are realizing as complex geometrical structures. Directorial surfaces are created on the basis of the specific set of rules, being a locus of points in space with the constant either sum of distances from predefined line directors. In this paper we derive the mathematical model for the particular directorial surfaces’ generation which seems to be suitable for cupola design. Representative Serbian buildings are analyzed and the possible reconstruction of their cupola are suggested.