Related papers: Tilings
The Taylor-Socolar tilings are regular hexagonal tilings of the plane but are distinguished in being comprised of hexagons of two colors in an aperiodic way. We place the Taylor-Socolar tilings into an algebraic setting which allows one to…
This note presents an interesting counterexample to a basic covering problem.
We consider a class of cut-and-project sets $\Lambda = \Lambda_F \times \zahl$ in the plane. Let $L=\Lambda+w\real$, $w\in\real^2$, be a countable union of parallel lines. Then either (1) $L$ is a discrete family of lines, (2) $L$ is a…
This text is an introduction to dilation surfaces. We attempt to expose some geometric and dynamical aspects of the subject: moduli spaces, directional foliations and the Teichm\"uller flow.
We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
The rapid emergence of airborne platforms and imaging sensors are enabling new forms of aerial surveillance due to their unprecedented advantages in scale, mobility, deployment and covert observation capabilities. This paper provides a…
An approach to hiding objects levitating or flying above a conducting sheet is suggested in this letter. The proposed device makes use of isotropic negative-refractive-index materials without extreme material parameters, and creates an…
An exposition of the basic geometry of twistor integrals, intended for mathematicians.
The study of the structure of translational tilings has captivated mathematicians, scientists, and the general public for centuries and continues to thrive at the crossroads of analysis, combinatorics, dynamics, logic, number theory, and…
For a locally finite set in $\mathbb{R}^2$, the order-$k$ Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of…
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral…
In the article "Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane" we constructed a compact topological space for the combinatorics of "A regular pentagonal tiling of the plane", which we…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
This paper numerically investigates the feasibility of lensless zoomable holographic multiple projections to tilted planes. We have already developed lensless zoomable holographic single projection using scaled diffraction, which calculates…
The purpose of this work is to explain how wings work and how they were invented. We use the lens of history, looking at the individual people who wanted to fly, the lens of technology, looking at the key inventions leading up to modern…
We give several new examples of hexagonal 3-webs of circles in the plane and give a survey on such webs.
In this paper we introduce a generalization of Hamiltonian mechanics that replaces configuration spaces, conventionally regarded simply as smooth manifolds, with line bundles over smooth manifolds. Classical observables are then identified…
We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.