Related papers: Creative geometry
We continue our discussion from part I.
A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.
We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.
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.…
This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same train of ideas, the article also provides a proof of the…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
One of the best things about geometry is that it's cool! Geometry enables us to create incredible designs and astounding patterns. This article shows how to use a simple technique (iteration) to create designs that are both cool and…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
The kinematics of particles and rigid bodies in the plane are investigated up to higher-order accelerations. Discussion of point trajectories leads from higher-order poles to higher-order Bresse circles of the moving plane. Symplectic…
This paper gives a first step towards developing synthetic differential geometry within homotopy type theory. Its model theory will be discussed in a subsequent paper.
Convex geometry and complex geometry have long had fascinating interactions. This survey offers a tour of a few.
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
The purpose of this paper is to present projective geometry in a synthetic, visual and intuitive style through the central notion of harmonicity which leads to harmonic curves. This presentation includes new results, unpublished proofs of…
We establish some new theorems on pentagon and pentagram.
We offer a new perspective on the closed graph theorem and the open mapping theorem for separated barrelled spaces and fully complete spaces.
The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…
This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.