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The Mercator projection is sometimes confused with another mapping technique, specifically the central cylindrical projection, which projects the Earth's surface onto a cylinder tangent to the equator, as if a light source is at the Earth's…

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 investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…

The method of alternating projections involves orthogonally projecting an element of a Hilbert space onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm if the projections are taken…

Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…

One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…

We investigate P. Halmos' two projections theorem, (or two subspaces theorem) in the context of a synaptic algebra (a generalization of the self-adjoint part of a von Neumann algebra).

We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic…

We present a method to project a hypercube of arbitrary dimension on the plane, in such a way as to preserve, as well as possible, the distribution of distances between vertices. The method relies on a Montecarlo optimization procedure that…

We highlight the relation between the projective geometries of $n$-dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the $n+1$-dimensional Minkowski space, using a cross ratio notion…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

Let $k$ and $i_1,\ldots,i_n$ be natural numbers. Place $k$ balls into a multidimensional box of $i_1\times\cdots \times i_n$ cells, no more than one ball to each cell, such that the projections to each of the coordinate axes have…

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general…

We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…

We will derive both quaternion and octonion algebras as the Clebsch-Gordan algebras based upon the su(2) Lie algebra by considering angular momentum spaces of spin one and three. If we consider both spin 1 and 1/2 states, then the same…

This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…

Two averaging algorithms are considered which are intended for choosing an optimal plane and an optimal circle approximating a group of points in three-dimensional Euclidean space.

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators - generalized Pauli matrices - characterizing two-qubit systems. The relevant…

This paper is the written version of our talk (presented by the second author) at the IWOTA in Chemnitz in August 2017. The meta theorem of the paper is that Halmos' two projections theorem is something like Robert Sheckley's Answerer: no…

The goal of this paper is to present two algorithms for solving systems of inclusion problems, with all component of the systems being a sum of two maximal monotone operators. The algorithms are variants of the forward-backward splitting…