Related papers: Some new theorems in plane geometry
Computations in renormalizable perturbative quantum field theories reveal mathematical structures which go way beyond the formal structure which is usually taken as underlying quantum field theory. We review these new structures and the…
This article gives an overview, aimed at theoretical particle physicists, of some recent developments in cosmology.
In this chapter, we report the recent progress in the understanding of the rich mathematical structures of topological insulators in the framework of index theory and noncommutative geometry.
New perspective form of equations for geodesic lines in Riemann Geometry was found. This method is based on the use of differential forms in differential equations as arguments of differentiation. At that, these forms do not have a…
We discuss the theorem on the existence of six points on a convex closed plane curve in which the curve has a contact of order six with the osculating conic. (This is the ``projective version'' of the well known four vertices theorem for a…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
In this paper, based on the theory of surfaces in the four-dimensional Euclidean space which generalizes the theory of surfaces in three-dimensional Euclidean space, beside other results, we will give a characterization of points on…
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
The paper aims to point out a novel geometric characterisation of the WDVV equations of 2D topological field theory.
This paper states and proves a generalization of the well-known Desargues involution theorem from plane projective geometry.
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
The goal of this paper is to give a purely geometric proof of a theorem by Branko Gr\"unbaum concerning configuration of triangles coming from the classical Napoleon's theorem in planar Euclidean geometry.
In this paper, we study the contribution of the theory of grossone to the study of infinigons in the hyperbolic plane. We can see that the theory of grossone can help us to obtain much more classification for these objects than in the…
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
In this paper we collect the main properties of free curves in the complex projective plane and a lot of conjectures and open problems, both old and new. In the quest to understand the mystery of free curves, many tools were developed and…
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.