Related papers: A Roman Dodecahedron for measuring distance
The distance between a pair of spike trains, quantifying the differences between them, can be measured using various metrics. Here we introduce a new class of spike train metrics, inspired by the Pompeiu-Hausdorff distance, and compare them…
Ancient instruments of high interest for research on the origin and diffusion of early scientific devices in the late XVI - early XVII centuries are reproduced in three paintings by Jan Brueghel the Elder. We investigated the nature and the…
Archaeological mirrors from the Olmec civilization were analyzed in the context of bibliography produced in the last two decades. Photographs of its images are showed as a proof of its good quality. Some suggestions are made on its probable…
Measuring the distance between data points is fundamental to many statistical techniques, such as dimension reduction or clustering algorithms. However, improvements in data collection technologies has led to a growing versatility of…
The TOTEM experiment has been designed to measure the total proton-proton cross section and to study the elastic and diffractive scattering at the LHC energy. The measurement requires detecting protons at distances as small as 1 mm from the…
Several authors have pointed out the connection between Barbilian's metric introduced in 1934 and the recent study of Apollonian metrics. We provide examples of various distances that can be obtained by Barbilian's metrization procedure and…
When robot manipulators decide how to reach for an object, hand it over, or obey some task constraint, they implicitly assume a Euclidean distance metric in their configuration space. Their notion of what makes a configuration closer or…
Recently it has been discovered that on a stone tablet over 3800 years old, the Plimpton-322 table, are carved the geometric relations that exist between the sides of 15 right triangles chosen in a very special way. Due to its property as a…
The idea of using measure theoretic concepts to investigate the size of number theoretic sets, originating with E. Borel, has been used for nearly a century. It has led to the development of the theory of metrical Diophantine approximation,…
Edge-to-edge interprecipitate distance distributions are critical for predicting precipitation strengthening of alloys and other physical phenomena. A method to calculate this 3D distance and the 2D interplanar distance from atom-probe…
Using Connes distance formula in noncommutative geometry, it is possible to retrieve the Euclidean distance from the canonical commutation relations of quantum mechanics. In this note, we study modifications of the distance induced by a…
We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to $\mathbb R^n$ equipped with a distance $(d_{\rm E})^\epsilon$, for some $n\in \mathbb N_0$ and $\epsilon\in (0,1]$, where $d_{\rm…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
This paper shows how to use the shooting method, a classical numerical algorithm for solving boundary value problems, to compute the Riemannian distance on the Stiefel manifold $\mathrm{St}(n,p)$, the set of $ n \times p $ matrices with…
In metric Diophantine approximation, one frequently encounters the problem of showing that a limsup set has positive or full measure. Often it is a set of points in $m$-dimensional Euclidean space, or a set of $n$-by-$m$ systems of linear…
Calling mammals, ships, and many other objects have been commonly located during the last century with two-dimensional (2D) models from measurements of signal time even when the objects are not on the 2D surface. The overwhelmingly common…
This paper describes the Duchamp source finder, a piece of software designed to find and describe sources in 3-dimensional, spectral-line data cubes. Duchamp has been developed with HI (neutral hydrogen) observations in mind, but is widely…
We demonstrate how the Fundamental Manifold (FM) can be used to cross-calibrate distance estimators even when those "standard candles" are not found in the same galaxy. Such an approach greatly increases the number of distance measurements…
The self-similarity of Indonesian Borobudur Temple is observed through the dimensionality of stupa that is hypothetically closely related to whole architectural body. Fractal dimension is calculated by using the cube counting method and…
I discuss various aspects of archeoastronomy concentrating on physical artifacts (i.e., not including ethno-archeoastronomy) focusing on the period that ended about 2000 years ago. I present examples of artifacts interpreted as showing the…