Results 211 to 220 of about 87,095 (251)

On Napoleon's theorem in the isotropic plane]{On Napoleon's theorem in the isotropic plane

Periodica Mathematica Hungarica, 2006
Napoleon's original theorem refers to arbitrary triangles in the Euclidean plane. If equilateral triangles are externally erected on the sides of a given triangle, then their three corresponding circumcenters form an equilateral triangle. We present some analogous theorems and related statements for the isotropic (Galilean) plane.
Horst Martini, Margarita Spirova, Martini Horst   +2 more
exaly   +3 more sources

On evolutes of curves in the isotropic plane

Aequationes Mathematicae
The Tait-Kneser theorem is a classical theorem which states that the osculating circles along a plane curve with monotone non-vanishing curvature are pairwise disjoint and nested. The main contribution of the paper is to prove a version of this theorem for curves in the isotropic plane.
Rui Pacheco
exaly   +2 more sources

Plane Cracks in a Transversely Isotropic Layer

Mechanics of Solids, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Artamonova, E. A., Pozharskii, D. A.
openaire   +2 more sources

Kiepert Triangles in an Isotropic Plane

Sarajevo Journal of Mathematics
In this paper the concept of the Kiepert triangle of an allowable triangle in an isotropic plane is introduced. The relationships between the areas and the Brocard angles of the standard triangle and its Kiepert triangle are studied. It is also proved that an allowable triangle and any of its Kiepert triangles are homologic.
Kolar-Šuper, Ružica, Kolar Begović, Zdenka, Volenec, Vladimir   +2 more
openaire   +3 more sources

Wrinkling of Plane Isotropic Biological Membranes

Journal of Applied Mechanics, 2006
The problem of the wrinkling of plane isotropic membranes characterized by a Fung type constitutive model in biaxial tension has been formulated and solved within the framework of finite strain hyperelasticity. The formulation follows the approach of Pipkin [Pipkin, A.C., 1986, IMA J. Appl. Math., 36, pp. 85–99; 1994, ibid., 52, pp.
MASSABO', ROBERTA, GAMBAROTTA, LUIGI
openaire   +1 more source

Thébault’s Pencil of Circles in an Isotropic Plane

Sarajevo Journal of Mathematics
In the Euclidean plane Griffiths's and Thébault's pencil of the circles are generally different. In this paper it is shown that in an isotropic plane the pencils of circles, corresponding to the Griffiths's and Thébault's pencil of circles in the Euclidean plane, coincide.
Volenec, Vladimir, Kolar-Šuper, Ružica, Kolar Begović, Zdenka   +2 more
openaire   +3 more sources

Isotropic Plane Elastostatics

2008
We begin with a uniqueness theorem in linear elastic doublet mechanics. With this tool in hand we present two methods of obtaining solutions. The first stems from a correspondence between problems in doublet and continuum mechanics which allows the generation of a solution in one theory given a solution in the other.
J. C. Nadeau, A. H. Nashat, M. Ferrari
openaire   +1 more source

Dual Feuerbach Theorem in an Isotropic Plane

Sarajevo Journal of Mathematics
The dual Feuerbach theorem for an allowable triangle in an isotropic plane is proved analytically by means of the so-called standard triangle. A number of statements about relationships between some concepts of the triangle and their dual concepts are also proved.
Kolar Begović, Zdenka, Volenec, Vladimir, Kolar-Šuper, Ružica   +2 more
openaire   +3 more sources