Related papers: Roman Dodecahedron as dioptron: analysis of freely…
Here I am discussing a possible use of a Roman Dodecahedron, a bronze artifact of gallo-roman origin, for measuring distance. A dodecahedron, found at Jublains, the ancient Nouiodunum, dating from the 2nd or 3rd century AD, is used to…
Rangefinders are instruments used for ballistics and for surveying in general. Here a short discussion of some of them, ranging from the ancient Rome to the modern methods.
The paper is proposing a short discussion on the ancient knowledge of Platonic solids, in particular, by Italic people.
A conjecture for the dimension and the character of the homogenous components of the free Jordan algebras is proposed. As a support of the conjecture, some numerical evidences are generated by a computer and some new theoretical results are…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
The random surfer model is a frequently used model for simulating user navigation behavior on the Web. Various algorithms, such as PageRank, are based on the assumption that the model represents a good approximation of users browsing a…
Astronomical observing has been greatly simplified by the development and implementation of digital imaging techniques and remote observing. Aperture photometry of CCD data permits photometric measurements to be made routinely with…
Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, - topology and number theory, - was built only during the last fifty years. This bridge is the theory of spectra in stable homotopy theory.…
This is a historian's view of how modern astronomy data can be used to discuss the shifting historical worldview of Late Antiquity. In this article an attemp is made to construct an approximate model of how the cycles of astronomical…
Retaining the combinatorial Euclidean structure of a regular icosahedron, namely the 20 equiangular (planar) triangles, the 30 edges of length 1, and the 12 different vertices together with the incidence structure, we investigate variations…
The coincidence problem for three-dimensional discrete structures with icosahedral symmetry is reinvestigated. We present a parametric description of the coincidence rotations based on special quaternions, called icosian numbers. In…
The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…
We propose a set of techniques leveraging mobile devices as lenses to explore, interact and annotate n-dimensional data visualizations. The democratization of mobile devices, with their arrays of integrated sensors, opens up opportunities…
In the analysis of three-dimensional biological microstructures such as organoids, microscopy frequently yields two-dimensional optical sections without access to their orientation. Motivated by the question of whether such random planar…
This entry contains the core material of my habilitation thesis, soon to be officially submitted. It provides a self-contained presentation of the original results in this thesis, in addition to their detailed proofs. The motivation of…
This paper constructs a Riemann surface associated to the icosahedron and discusses the geodesics associated to a flat metric on this surface. Because of the icosahedral symmetry, this is a distinguished special case of the example treated…
The NASA Nancy Grace Roman Space Telescope (Roman) and the Vera C. Rubin Observatory Legacy Survey of Space and Time (Rubin), will transform our view of the wide-field sky, with similar sensitivities, but complementary in wavelength,…
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
Pythagoras' theorem, the area of a triangle as one half the base times the height, and Heron's formula are amongst the most important and useful results of ancient Greek geometry. Here we look at all three in a new and improved light, using…
We place the theory of metric Diophantine approximation on manifolds into a broader context of studying Diophantine properties of points generic with respect to certain measures on $\Bbb R^n$. The correspondence between multidimensional…