Results 1 to 10 of about 87,095 (251)

Curves Related to the Gergonne Point in an Isotropic Plane

Mathematics, 2023
The notion of the Gergonne point of a triangle in the Euclidean plane is very well known, and the study of them in the isotropic setting has already appeared earlier. In this paper, we give two generalizations of the Gergonne point of a triangle in the isotropic plane, and we study several curves related to them.
Ema Jurkin, Marija SIMIĆ Horvath, Jurkin Ema   +2 more
exaly   +5 more sources

Parabolas in the isotropic plane

Glasnik matematički, 2021
In this paper we study the properties of a parabola in an isotropic plane and compare the results obtained with their Euclidean analogues.
Volenec, Vladimir, Jurkin, Ema, Šimić Horvath, Marija   +2 more
openaire   +6 more sources

Bisectors of conics in isotropic plane

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2023
In this paper we introduce the concept of a bisector of two curves in an isotropic plane. We study the bisectors of conics and classify them according to their type of circularity. In general the bisector of conics is a quartic, while in the case when both conics are circular, its degree decreases.
Ema Jurkin, Jurkin, Ema
openaire   +4 more sources

Circles of Curvature at Points of Parabola in Isotropic Plane [PDF]

Mathematica Pannonica, 2021
The authors have studied the curvature of the focal conic in the isotropic plane and the form of the circle of curvature at its points has been obtained. Hereby, we discuss several properties of such circles of curvature at the points of a parabola in the isotropic plane.
Volenec, Vladimir, Horvath, Marija Šimić, Jurkin, Ema   +2 more
openaire   +6 more sources

APOLLONIUS CIRCLES OF THE TRIANGLE IN AN ISOTROPIC PLANE

Taiwanese Journal of Mathematics, 2008
The concept of Apollonius circle and Apollonius axes of an allowable triangle in an isotropic plane will be introduced. Some statements about relationships between introduced concepts and some other previously studied geometric concepts about triangle will be investigated in an isotropic plane and some analogies with the Euclidean case will be also ...
Vladimir Volenec
exaly   +5 more sources

Morley’s triangles of a triangle in the isotropic plane

Journal of Geometry
Morley's trisector theorem is one of the most intriguing results of elementary triangle geometry. Adjacent trisectors of interior triangle angles intersect in three points of an equilateral triangle. Taking into account the ambiguity when considering angle trisectors of pairs of lines one can extend this result to a more complete picture with 18 ...
Vladimir Volenec, Ruzica Kolar-Šuper
exaly   +3 more sources

Hamilton Triangle of a Triangle in the Isotropic Plane [PDF]

Mathematica Pannonica, 2022
In this paper we introduce the concept of the Hamilton triangle of a given triangle in an isotropic plane and investigate a number of important properties of this concept. We prove that the Hamilton triangle is homological with the observed triangle and with its contact and complementary triangles. We also consider some interesting statements about the
Kolar Begović, Zdenka, Volenec, Vladimir   +1 more
openaire   +1 more source

Harmonic quadrangle in isotropic plane [PDF]

TURKISH JOURNAL OF MATHEMATICS, 2018
The concept of the harmonic quadrangle and the associated Brocard points are introduced and investigated in the isotropic plane by employing suitable analytic methods.
Jurkin, Ema, Šimić Horvath, Marija, Volenec, Vladimir, Beban-Brkić, Jelka   +3 more
openaire   +3 more sources

Gob’s Circles of a Triangle in the Isotropic Plane [PDF]

Journal of Mathematics, 2021
In this paper, we consider Gob’s circles of an allowable triangle in the isotropic plane and derive their equations in the case of a standard triangle. We prove that the potential axes of the circumscribed circle and Gob’s circles are the angle bisectors of the given triangle.
openaire   +3 more sources

On the Feuerbach Point and Feuerbach Line in the Isotropic Plane

Mathematica Pannonica, 2023
In this paper, we consider the Feuerbach point and the Feuerbach line of a triangle in the isotropic plane, and investigate some properties of these concepts and their relationships with other elements of a triangle in the isotropic plane. We also compare these relationships in Euclidean and isotropic cases.
Kolar-Šuper, Ružica, Volenec, Vladimir
openaire   +1 more source