相关论文: Arbitrary Sectioning of Angles in Taxicab Geometry
Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical design sparsity and accuracy. We show how to obtain sparse…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational…
This work discusses an approach to solving geometric construction problems in which the given figure is included in a set ordered by construction steps. The flow of information is carried through the chain, allowing the original problem to…
Let a polygon be composed of equal rectangles. We find all quadratic irrationals r for which the polygon can be tiled by similar rectangles with given side ratio r.
Given a bichromatic point set $P=\textbf{R} \cup \textbf{B}$ of red and blue points, a separator is an object of a certain type that separates $\textbf{R}$ and $\textbf{B}$. We study the geometric separability problem when the separator is…
Geometric mechanics is usually studied in applied mathematics and most introductory texts are hence aimed at a mathematically minded audience. The present note tries to provide the intuition of geometric mechanics and to show the relevance…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
We give some concrete constructions of real equiangular line sets. The emphasis here is on {\em building blocks} for certain angles which are then used to build up larger equiangular line sets. We concentrate on angles greater than or equal…
We prove an effective equidistribution result about angles in a hyperbolic lattice. We use this to generalize a result due to F. P. Boca.
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…
We construct a set of points with $\Omega(n^2\log n)$ triples determining an angle $\theta$ whenever $\tan(\theta)$ is algebraic over $\mathbb{Q}$, matching the upper bound of Pach and Sharir. This improves upon the original construction,…
In this paper, we introduce and study "geometric simultaneous RAC drawing problems", i.e., a combination of problems on geometric RAC drawings and geometric simultaneous graph drawings. To the best of our knowledge, this is the first time…
In this paper, we remind previous results about the tilings $\{p,q\}$ of the hyperbolic plane. We introduce two new ways to split the hyperbolic plane in order to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.
A short survey on applications of algebraic geometry in topological data analysis.
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the…
The convex feasibility problem asks to find a point in the intersection of a collection of nonempty closed convex sets. This problem is of basic importance in mathematics and the physical sciences, and projection (or splitting) methods…