Related papers: A Roman Dodecahedron for measuring distance
Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…
This article proposes a mathematical model of an inverted analemmatic sundial, provides formulas for calculating the coordinates of their hour markers. On the example of the Belogorsk sundial, a method is described for determining the…
Ratios and coefficients are used to simplify calculations. For geometric usage these values also called function values. Like in Egypt also in Babylon such a value system can be shown. The reconstructed calculation sequence, of the Plimpton…
A homogeneous set of $n$ points in the $d$-dimensional Euclidean space determines at least $\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)$ distinct distances for a constant $c(d)>0$. In three-space, we slightly improve our general bound and show…
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…
It is straightforward to determine the size of the Earth and the distance to the Moon without making use of a telescope. The methods have been known since the 3rd century BC. However, few amateur or professional astronomers have worked this…
Cooking possesses a system of units of measurement, that includes measures of volumes based on pre-metric units. This paper discusses the cooking measures and compares their features with those of the ancient Roman measures of capacity.
As is well known, classical systems approximate quantum ones -- but how well? We introduce a definition of a "distance" on classical and quantum phase spaces that offers a measure of their separation. Such a distance scale provides a means…
We prove that if two finitely generated groups act on a metrically complete 2-dimensional Euclidean building, then the distance between their fixed-point sets is realised. Our proof uses the geometry of Euclidean buildings, which we view as…
Exactly 500 years ago, Nicolaus Copernicus drew a lattice of lines on a panel above the doorway to his rooms at Olsztyn Castle, then in the Bishopric of Warmia. Although its design has long been regarded as some kind of reflecting vertical…
For almost twenty years, a search for a Lorentzian version of the well-known Connes' distance formula has been undertaken. Several authors have contributed to this search, providing important milestones, and the time has now come to put…
In this paper, we propose a novel penetration metric, called deformable penetration depth PDd, to define a measure of inter-penetration between two linearly deforming tetrahedra using the object norm. First of all, we show that a distance…
This article presents the results of a study of signs on a Bronze Age slab discovered in the vicinity of a heavily plowed mound near the settlement of Pyatikhatki. The slab belongs to the Dolmen archaeological culture. In the course of this…
This paper defines a distance function that measures the dissimilarity between planar geometric figures formed with straight lines. This function can in turn be used in partial matching of different geometric figures. For a given pair of…
One reason that the planet Neptune will be remembered for, is to do with the fact that it was the first planet whose existence was postulated before being observed. This was based on analysing deviations in Uranus' orbit. The present study…
The distance modulus of the Large Magellanic Cloud (LMC) is the first step on the determination of the cosmic distance scale. In this paper it is obtained from a new calibration of the classical Cepheid Period-Luminosity (PL) relation. Our…
Chameleons are a well motivated scalar field that might explain the observed late time accelerated expansion of the universe. Chameleons possess the interesting property that their mass, and hence interaction range, is dependent on the…
Sundials and gnomons pointing out dates and times are a beautiful reminder of how we understand the movement of the Sun and use it to structure day and year. They also encapsulate the basic astronomical knowledge and concepts of the…
This study reconstructs the origin of a constant, here called $\Xi$ (Xi), as a primary scaling factor in Old Babylonian mathematics and astronomy. $\Xi$ arises from the practical necessity of precise measurements on the sky or a circle,…