OpisIn this paper we examine the shape of a triangle by means of a ternary operation which satisfies some properties. We prove that each system of the shapes of triangles can be obtained by means of the field with defined ternary operation. We give a geometric model of the shapes of triangles on the set of complex numbers which motivate us to introduce some geometric concepts. The concept of transfer is defined and some interesting properties are explored. By means of transfer the concept of a parallelogram is introduced.
OpisIn the paper the concept of a covertex inscribed triangle of a parabola in an isotropic plane is introduced. It is a triangle inscribed to the parabola that has the centroid on the axis of parabola, i.e. whose circumcircle passes through the vertex of the parabola. We determine the coordinates of the triangle centers, and the equations of the lines, circles and conics related to the triangle. U radu se uvodi pojam covertex trokuta upisanog paraboli u izotropnoj ravnini. To je trokut upisan paraboli čije težište leži na osi parabole, tj. čija opisana kružnica prolazi tjemenom parabole. Određuju se koordinate točaka te jednadžbe pravaca, kružnica i konika povezanih s tim trokutom.
OpisIn this paper, we examine the Jerabek hyperbola of an allowable triangle in an isotropic plane. We investigate different ways of generating this special hyperbola and derive its equation in the case of a standard triangle in an isotropic plane. We prove that some remarkable points of a triangle in an isotropic plane lie on that hyperbola whose centre is at the Feuerbach point of a triangle. We also explore other interesting properties of this hyperbola and its connection with some other significant elements of a triangle in an isotropic plane. U radu proučavamo Jerabekovu hiperbolu dopustivog trokuta u izotropnoj ravnini. Istražujemo različite načine generiranja ove specijalne hiperbole i izvodimo njenu jednadžbu u slučaju standardnog trokuta. Dokazujemo da neke značajne točke trokuta u izotropnoj ravnini leže na toj hiperboli čiji je centar u Feuerbachovoj točki trokuta. Proučavamo i neka druga zanimljiva svojstva ove hiperbole i njezinu vezu s nekim značajnim elementima trokuta u izotropnoj ravnini.
OpisIn this paper we study geometric concepts in a general cubic structure. The well-known relationships on the cubic curve motivate us to introduce new concepts into a general cubic structure. We will define the concept of the tangential of a point in a general cubic structure and we will study tangentials of higher-order. The characterization of this concept will be also given by means of the associated totally symmetric quasigroup. We will introduce the concept of associated and corresponding points in a cubic structure, and discuss the number of mutually different corresponding points. The properties of the introduced geometric concepts will be investigated in a general cubic structure.