Related papers: Geometry and Design of Equiangular Spirals
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
A four dimensional description for the trigonal phase is presented. It has been demonstrated that it is possible to model one dimensional quasiperiodic structure with trigonal symmetry apart from recovering the Miller-Bravais scheme for the…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
From the geometric study of the elementary cell of hexagonal circle packings --- a flower of 7 circles --- the class of conformally symmetric circle packings is defined. Up to Moebius transformations, this class is a three parameter family,…
An unfolding of a polyhedron is produced by cutting the surface and flattening to a single, connected, planar piece without overlap (except possibly at boundary points). It is a long unsolved problem to determine whether every polyhedron…
We survey partial geometric designs and investigate their concurrences of points. The concurrence matrix of a design, which encodes the concurrences of pairs of points, can be used in the classification of designs in some extent. An…
We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we…
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…
Curves in ${\mathbb R}^n$ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For $n= 3,4$, spherical curves of this kind are also…
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…
The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally…
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
In this article, we provide some necessary and sufficient coefficients conditions for a harmonic mapping to be hereditarily spirallike. Also, we give growth estimate for certain harmonic hereditarily spirallike mappings. Moreover, we…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
Hexagonal circle patterns with constant intersection angles are introduced and studied. It is shown that they are described by discrete integrable systems of Toda type. Conformally symmetric patterns are classified. Circle pattern analogs…
Chemical gardens are mineral aggregates that grow in three dimensions with plant-like forms and share properties with self-assembled structures like nano-scale tubes, brinicles or chimneys at hydrothermal vents. The analysis of their shapes…
A method to construct transition curves using a family of the quartic Bezier spiral is described. The transition curves discussed are S-shape and C-shape of contact, between two separated circles. A spiral is a curve of monotone increasing…
We use high resolution 2D hydrodynamic simulations to study the formation of spiral substructure in the gaseous disk of a galaxy. The obtained gaseous response is driven by a self-consistent non-axisymmetric potential obtained from an…
In this article, we discuss the equality of two inner products on a vector space. Particularly, we look at some geometric properties that are given to a vector space by an inner product namely, length and angle, and we ask under what…
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…