Related papers: A Roman Dodecahedron for measuring distance
We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the…
This paper presents a general approach for measuring distances between board games within the Ludii general game system. These distances are calculated using a previously published set of general board game concepts, each of which…
In this note we study the displacement function $d_g(x):=d(gx,x)$ of an isometry $g$ of a Euclidean building. We give a lower bound for $d_g(x)$ depending on the distance from $x$ to the minimal set of $g$.
Liquid argon technology is widely used by many previous and current neutrino experiments, and it is also promising for future large-scale neutrino experiments. When detecting neutrinos using liquid argon, many hadrons are involved, which…
This research paper aims to compare different methods for calculating the distance to the Large Magellanic Cloud (\textit{LMC}). The distance, $d_{LMC}$, is determined using stellar parallax, variable stars (RR Lyrae and Classical…
Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…
In 1738, the King of Naples and future King of Spain, Carlos III, commissioned the Spanish military engineer Roque Joaqu\'in de Alcubierre to begin the excavations of the ruins of the ancient Roman city of Pompeii and its surroundings,…
We investigate two-dimensional, periodic ornaments of the Late Hellenistic (some centuries before the Common Era, the Classical Period) and Early Roman (Common Era) classical periods found at different locations in Asia Minor in Turkey and…
It will be shown that the rotation of the Earth in the Earth-Moon system can be detected by comparing the deflection of a Foucault pendulum at noon on the one hand and at midnight on the other hand. More precisely, on 21 June the midnight…
Astronomers measure cosmic distances to objects beyond our own galaxy using standard candles: objects of known intrinsic brightness, whose apparent brightnesses in the sky are then taken as an indication of their distances from the…
The AMADEUS system is integrated in the ANTARES neutrino telescope in the Mediterranean Sea and aims for the investigation of acoustic particle detection techniques in the deep sea. Installed at a depth of more than 2000m, the acoustic…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
There is renewed interest in using advanced techniques to characterize ancient Roman concrete. In the present work, samples were drilled from the "Hospitium" in Pompeii and were analyzed by synchrotron microtomography (uCT) and neutron…
The Clementine Gnomon is a giant pinhole dark camera dedicated to meridian solar astrometry operating in the Basilica of Santa Maria degli Angeli in Rome. Pope Clement XI ordered Francesco Bianchini (1662-1729) to build this instrument in…
Parallelograms are one of the basic building blocks in two-dimensional tiling. They have important applications in a wide variety of science and engineering fields, such as wireless communication networks, urban transportation, operations…
Large-scale neutrino telescopes have the primary objective to detect and characterize neutrino sources in the universe. These experiments rely on the detection of charged leptons produced in the interaction of neutrinos with nuclei. Angular…
This paper presents a hands-on introduction to the medieval astrolabe, based around a working model which can be constructed from photocopies of the supplied figures. As well as describing how to assemble the model, I also provide a brief…
Distance measures are indispensable tools in quantum information processing and quantum computing. This since they can be used to quantify to what extent information is preserved, or altered, by quantum processes. In this paper we propose a…
Classical Cepheids were the first stellar standard candles and have played a crucial role for astronomical distance measurements ever since the discovery of the Leavitt law (period-luminosity relation). Enormous improvements in distance…
The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean…