Related papers: Elementary Surprises in Projective Geometry
This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.
We present two new constructions in the usual euclidean plane. We only deal with 'Grecian Geometry', with this phrase we mean elementary geometry in the two-dimensional space R 2 . We describe and prove two propositions about 'projections'.…
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
Of the great theories of classical mathematics, projective geometry, with its powerful concepts of symmetry and duality, has been exceptional in continuing to intrigue investigators. The challenge put forth by Errett Bishop (1928-1983),…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Our research is motivated by recent work of Cook II, Harbourne, Migliore, and Nagel on configurations of points in the projective plane with properties that are unexpected from the point of view of the postulation theory. In this note, we…
The classical theory of plane projective geometry is examined constructively, using both synthetic and analytic methods. The topics include Desargues's Theorem, harmonic conjugates, projectivities, involutions, conics, Pascal's Theorem,…
We deal with generalizations of the Fundamental Theorem of Projective Geometry to other related geometries (of dimension $\geq 3$) and non bijective maps. We consider locally projective geometries and locally affino-projective geometries…
We discuss various phenomena of tangency in projective and convex geometry.
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
In 1640's, Blaise Pascal discovered a remarkable property of a hexagon inscribed in a conic - Pascal Theorem, which gave birth of the projective geometry. In this paper, a new geometric invariant of algebraic curves is discovered by a…
In this paper, we investigate the configuration theorems of Desargues and Pappus in a synthetic geometric way. We provide a bridge between the two configurations with a third one that can be considered a specification for both. We do not…
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 show that various classical theorems of real/complex linear incidence geometry, such as the theorems of Pappus, Desargues, M\"obius, and so on, can be interpreted as special cases of a single "master theorem" that involves an arbitrary…
A new mneumonic device is shown to emerge in connection with O(7) numerical tensors exhibiting duality and reflecting the natural 7=(4+3) splitting of 7-dimensional space. Then Desargues' and Pappus' theorems are shown to be connected…
Results on $8$-dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…