相关论文: Arbitrary Sectioning of Angles in Taxicab Geometry

The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…

We discuss the principle tools and results and state a few open problems concerning the classification and topology of plane sextics and trigonal curves in ruled surfaces.

A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…

Isoparametric hypersurfaces and their application to special geometries

Using the language of stacks, we recast and generalize a selection of results in equivariant geometry.

We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…

We study the construction of substitution tilings of the plane based on certain simplicial configurations of tangents of the deltoid with evenly distributed orientations. The random tiling ensembles are obtained as a result of tile…

We review, from a didactic point of view, the definition of a toric section and the different shapes it can take. We'll then discuss some properties of this curve, investigate its analogies and differences with the most renowned conic…

We suggest a method of solving the problem of existence of a triangle with prescribed two bisectors and one third element which can be taken as one of the angles, the sides, the heights or the medians, or the third bisector.

We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle…

Trisecting an angle has been proved to be impossible by Euclidean Geometry, using only straight edge and compass. However, there is a method using Origami (paper folding) procedure to trisect an angle. The algebraic analysis of the same…

We determine the conditions resulting from equating the area sums of alternative sectors in a circle generated by four, two, and three straight lines, respectively, that connect opposite points on its circumference while passing through a…

A general method for analytic inversion of geometric integral transforms is proposed

We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.

We construct affine algebras with an arbitrary amount of simple modules of each dimension.

We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good…

Edge casing is a well-known method to improve the readability of drawings of non-planar graphs. A cased drawing orders the edges of each edge crossing and interrupts the lower edge in an appropriate neighborhood of the crossing. Certain…

An $N$-dimensional parallelepiped will be called a bar if and only if there are no more than $k$ different numbers among the lengths of its sides (the definition of bar depends on $k$). We prove that a parallelepiped can be dissected into…

Fix two points $p$ and $q$ in the plane and a positive number $k \neq 1$. A result credited to Apollonius of Perga states that the set of points $x$ that satisfy $d(x, p)/d(x, q) = k$ forms a circle. In this paper we study the analogous set…

The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…