Related papers: Constructive projective extension of an incidence …
The evolute of a curve is the envelope of its normals. In this note we consider a projectively natural discrete analog of this construction: we define projective perpendicular bisectors of the sides of a polygon in the projective plane, and…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We…
Finite projective planes are constructed using groups that satisfy simple-looking conditions. The resulting projective planes include many known planes and possibly new ones, and are precisely those having a collineation group fixing a flag…
There is no field with only one element, yet there is a well-defined notion of what projective geometry over such a field means. This notion is familiar to experts and plays an interesting role behind the scenes in combinatorics and…
Here we investigate the birational geometry of projective varieties of arbitrary dimension having defective higher secant varieties. We apply the classical tool of tangential projections and we determine natural conditions for uniruledness,…
Projective structures on compact real manifolds are classical objects in real differential geometry. Complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than…
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…
It is proved that for a 3-dimensional compact metrizable space X the infinite real projective space is an absolute extensor of X if and only if the real projective plane is an absolute extensor of X.
We will use toric degenerations of the projective plane ${{\mathbb{P}}^ 2}$ to give a new proof of the triple points interpolation problems in the projective plane. We also give a complete list of toric surfaces that are useful as…
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra…
We formulate a theory of shape valid for objects of arbitrary dimension whose contours are path connected. We apply this theory to the design and modeling of viable trajectories of complex dynamical systems. Infinite families of…
The "Perpendicular Bisectors Construction" is a natural way to seek a replacement for the circumcenter of a noncyclic quadrilateral in the plane. In this paper, we generalize this iterative construction to a construction on polytopes with…
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivated by applications in several areas of applied analysis, we…
Euclidean geometry consists of straightedge-and-compass constructions and reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. We consider three versions of…
In this paper we give a generalization of injective and projective complexes.
Any set of $\sigma$-Hermitian matrices of size $n \times n$ over a field with involution $\sigma$ gives rise to a projective line in the sense of ring geometry and a projective space in the sense of matrix geometry. It is shown that the two…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…