Related papers: Two Strange Constructions in the Euclidean Plane

This paper shows how a recent reformulation of the basics of classical geometry and trigonometry reveals a three-fold symmetry between Euclidean and non-Euclidean (relativistic) planar geometries. We apply this chromogeometry to look at…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

In algebraic topology, we usually represent surfaces by mean of cellular complexes. This representation is intrinsic, but requires to identify some points through an equivalence relation. On the other hand, embedding a surface in a…

In this paper, orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal…

The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some…

A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We…

We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…

A geometric realization of the projective completion of the Jordan pair corresponding to a three-graded Lie algebra is given which permits to develop a geometric structure theory of the projective completion. This will be used in Part II of…

We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of…

We describe elementary transformations between minimal models of rational surfaces in terms of unprojections. These do not fit into the framework of Kustin-Miller unprojections as introduced by Papadakis and Reid, since we have to leave the…

It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…

Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.

In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…

In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The…

We collect together various facts about G_2 and Spin(7) geometry which are likely well known but which do not seem to have appeared explicitly in the literature before. These notes should be useful to graduate students and new researchers…

We study surfaces in Euclidean space constructed by the sum of two curves or that are graphs of the product of two functions. We consider the problem to determine all these surfaces with constant Gauss curvature. We extend the results to…

In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…

This paper combines two classical theories, namely metric projective differential geometry and superintegrability. We study superintegrable systems on 2-dimensional geometries that share the same geodesics, viewed as unparametrized curves.…

The two-dimensional surface of a bi-axial ellipsoid is characterized by the lengths of its major and minor axes. Longitude and latitude span an angular coordinate system across. We consider the egg-shaped surface of constant altitude above…