Concept

Pappus's hexagon theorem

Related publications (10)

On the existence of ordinary triangles

Sebastian Urban Stich, Radoslav Fulek, Márton Naszódi

Let P be a finite point set in the plane. A \emph{c-ordinary triangle} in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question o ...

Elsevier2017

The effect of “objecthood” in the Ebbinghaus illusion

Michael Herzog, Aline Françoise Cretenoud, Einat Rashal

In the Ebbinghaus illusion, observers overestimate the size of a target when it is surrounded by large flakers and compared with a control target surrounded by small flankers. We examined whether “objecthood” – the degree to which an object is a cohesive e ...

2017

Large subsets of discrete hypersurfaces in Z d contain arbitrarily many collinear points

Florian Karl Richter

In 1977 L.T. Ramsey showed that any sequence in Z 2 with bounded gaps contains arbitrarily many collinear points. Thereafter, in 1980, C. Pomerance provided a density version of this result, relaxing the condition on the sequence from having bounded gaps t ...

2016

A note on coloring line arrangements

János Pach, Rom Pinchasi

We show that the lines of every arrangement of n lines in the plane can be colored with O(root n/log n) colors such that no face of the arrangement is monochromatic. This improves a bound of Bose et al. by a circle minus(root/log n) factor. Any further imp ...

Electronic Journal Of Combinatorics2014

Derivation of spin-orbit couplings in collinear linear-response TDDFT: A rigorous formulation

Ivano Tavernelli, Basile Curchod, Thomas James Penfold

Using an approach based upon a set of auxiliary many-electron wavefunctions we present a rigorous derivation of spin-orbit coupling (SOC) within the framework of linear-response time-dependent density functional theory (LR-TDDFT). Our method is based on a ...

2014

Chromatin architectures and hox gene collinearity

Denis Duboule, Daniël Noordermeer

Ever since the observation that collinearity, that is, the sequential activity of Hox genes based on their relative positions within their gene clusters, is conserved throughout most of the animal kingdom, the question has been raised as to what are the un ...

Elsevier Academic Press Inc2013

Phase diagram of the spin-1 Heisenberg model with three-site interactions on the square lattice

Frédéric Mila, Frédéric Alexis Michaud

We study the spin S = 1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S-i . S-j)(S-j . S-k) + H.c. This interaction appears naturally in a strong coupli ...

2013

On the connectivity of visibility graphs

The visibility graph of a finite set of points in the plane has the points as vertices and an edge between two vertices if the line segment between them contains no other points. This paper establishes bounds on the edge- and vertex-connectivity of visibil ...

2011

Two-dimensional tetramer-cuprate Na5RbCu4(AsO4)4Cl2: phase transitions and AFM order as seen by 87Rb NMR

Wendy Lee Queen

We report the 87Rb NMR results in a recently synthesized Na5RbCu4(AsO4)Cl2. This complex novel two-dimensional (2D) cuprate is an unique magnetic material, which contains layers of coupled Cu4O4 tetramers. In zero applied magnetic field, it orders antiferr ...

2006

Serial deletions and duplications suggest a mechanism for the collinearity of Hoxd genes in limbs

Denis Duboule

Hox genes, located at one end of the HoxD cluster, are essential for the development of the extremities of our limbs; that is, the digits. This 'collinear' correspondence is accompanied by a gradual decrease in the transcriptional efficiency of the genes. ...

2002

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