Related papers: Some Geometric Properties of the Yff Points of a T…
The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to…
The first isodynamic point of a triangle is one of many notable points associated with a triangle. It is named X(15) in the Encyclopedia of Triangle Centers. This paper surveys known results about this point and gives additional properties…
We give three new proofs of the triangle inequality in Euclidean Geometry. There seems to be only one known proof at the moment. It is due to properties of triangles, but our proofs are due to circles or ellipses. We aim to prove the…
This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…
Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…
An old theorem of Alexander Soifer's is the following: Given five points in a triangle of unit area, there must exist some three of them which form a triangle of area 1/4 or less. It is easy to check that this is not true if "five" is…
The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of \emph{strange attractors}. However Lorenz' research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the…
The fixed-point theory and its applications to various areas of science are well known. In this paper we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We…
The theory of $F$-manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and…
Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…
The geometrisation theorem of 3-manifolds was conjectured by Thurston the 1980s and proved by Perelman in the 2000s. This is an overview on the subject. We explain the content of the theorem and describe its effects in various situations.
\"{O}zavsar and Cevikel(Fixed point of multiplicative contraction mappings on multiplicative metric space.arXiv:1205.5131v1 [math.GN] 23 may 2012)initiated the concept of the multiplicative metric space in such a way that the usual…
We first introduce a configuration of arbitrary isogonal conjugates related to a known property concerning the spiral center of two pairs of isogonal conjugates. We then consider a special case where two conics are tangent at exactly two…
Tight-spans of metrics were first introduced by Isbell in 1964 and rediscovered and studied by others, most notably by Dress, who gave them this name. Subsequently, it was found that tight-spans could be defined for more general maps, such…
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
We examine quadratic surfaces in 3-space that are tangent to nine given figures. These figures can be points, lines, planes or quadrics. The numbers of tangent quadrics were determined by Hermann Schubert in 1879. We study the associated…
We give a brief introduction to some of the recent works on finding geometric structures on triangulated surfaces using variational principles.
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is…
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of…