Results 1 to 10 of about 34 (31)

On Some Properties of the First Brocard Triangle in the Isotropic Plane

Mathematics, 2022
In this paper we introduce the first Brocard triangle of an allowable triangle in the isotropic plane and derive the coordinates of its vertices in the case of a standard triangle.
Vladimir Volenec, Zdenka Kolar-Begović, Ruzica Kolar-Šuper   +2 more
exaly   +3 more sources

Limit shape of iterated Kiepert triangles

Elemente der Mathematik, 2014
The authors consider a discrete dynamical system defined in the following way: Starting with a base triangle \(\Delta_0=ABC\), erect externally on all sides of \(\Delta_0\) similar isosceles triangles with apex angle \(\pi-2\theta_0\). The apices opposite to \(A\), \(B\) and \(C\), say, \(A_1,B_1,C_1\) determine the \textit{Kiepert triangle} \(\Delta_1\
Nicollier, Grégoire, Stadler, Albert
openaire   +2 more sources

Kiepert hyperbola of a triangle in an isotropic plane

Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2018
The concept of the Kiepert hyperbola of an allowable triangle in an isotropic plane is introduced in this paper. Important properties of the Kiepert hyperbola will be investigated in the case of the standard triangle. The relationships between the introduced concepts and some well known elements of a triangle will also be studied.
Volenec, Vladimir, Kolar-Begović, Zdenka, Kolar-Šuper, Ružica   +2 more
openaire   +2 more sources

The stationary focus of the Kiepert parabola over a special Poncelet triangle family

CoRR
We show that the focus of the Kiepert in-parabola remains stationary over a family of circle-inscribed Poncelet triangles which contain an equilateral triangle.
Mark Helman, Ronaldo Garcia, Dan Reznik
openaire   +2 more sources

On Yiu's Equilateral Triangles Associated with a Kiepert Hyperbola

, 2019
In 2014, Paul Yiu constructed two equilateral triangles inscribed in a Kiepert hyperbola associated with a reference triangle. It was asserted that each of the equilateral triangles is triply perspective to the reference triangle, and in each case, the corresponding three perspectors are collinear.
openaire   +2 more sources

Exploring surface water as a transmission medium of avian influenza viruses - systematic infection studies in mallards. [PDF]

Emerg Microbes Infect, 2022
Ahrens AK, Selinka HC, Mettenleiter TC, Beer M, Harder TC.   +4 more
europepmc   +1 more source

On Yiu’s Equilateral Triangles Associated with a Kiepert Hyperbola

Geometry
In 2014, Paul Yiu constructed two equilateral triangles inscribed in a Kiepert hyperbola associated with a reference triangle. It was asserted that each of the equilateral triangles is triply perspective with the reference triangle, and in each case, the corresponding three perspectors are collinear.
openaire   +1 more source

Substituent effect in determining the total structure of an all-alkynyl-protected Ag₉₈ nanocluster for methanol tolerant oxygen reduction reaction. [PDF]

Chem Sci
Cui X, Zhang X, Li T, Zhu S, Han G, Li H.   +5 more
europepmc   +1 more source

The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle

Mathematics Magazine, 1994
(1994). The Conics of Ludwig Kiepert: A Comprehensive Lesson in the Geometry of the Triangle. Mathematics Magazine: Vol. 67, No. 3, pp. 188-205.
R. H. Eddy, R. Fritsch
exaly   +4 more sources