Related papers: Solid angles in perspective
Universal Design (UD), an approach to accessibility that was first conceptualized in architecture to make buildings physically accessible, has since been applied to curriculum design to make classrooms accessible for a larger range of…
The International System of Units (SI) is supposed to be coherent. That is, when a combination of units is replaced by an equivalent unit, there is no additional numerical factor. Here we consider dimensionless units as defined in the SI,…
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the…
We introduce the notion of order projections using the order unit property of a positive element in an order unit space and characterize them in terms of (geometric) orthogonality. We describe order projections of the order unit space…
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.
The problem of fundamental units is discussed in the context of achievements of both theoretical physics and modern metrology. On one hand, due to fascinating accuracy of atomic clocks, the traditional macroscopic standards of metrology…
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Calculating the structure of white dwarf and neutron stars would be a suitable topic for an undergraduate thesis or an advanced special topics or independent study course. The subject is rich in many different areas of physics accessible to…
Consider a random $d$-dimensional simplex whose vertices are $d+1$ random points sampled independently and uniformly from the unit sphere in $\mathbb R^d$. We show that the expected sum of solid angles at the vertices of this random simplex…
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…
In 2019 the International System of units (SI) conceptually re-invented itself. This was necessary because quantum-electronic devices had become so precise that the old SI could no longer calibrate them. The new system defines values of…
We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…
We present herewith certain thoughts on the important subject of nowadays physics, pertaining to the so-called ``singularities'', that emanated from looking at the theme in terms of ADG (: abstract differential geometry). Thus, according to…
Plans are underway to redefine the International System of Units (SI) around 2018. The New SI specifies the values of certain physical constants to define units. This article explains the New SI in a way that could be used to present it to…
We provide some historical context to the study of solid angles carried out by Euler in his memoir \emph{De mensura angulorum solidorum} (On the measure of solid angles). We extend our study to the general notion of angle (not only solid).…
We propose a covariant and geometric framework to introduce space distances as they are used by astronomers. In particular, we extend the definition of space distances from the one used between events to non-test-bodies with horizons and…
Spectroscopy is one of the most important tools that an astronomer has for studying the universe. This chapter begins by discussing the basics, including the different types of optical spectrographs, with extension to the ultraviolet and…
The orientation of a rigid object can be described by a rotation that transforms it into a standard position. For a symmetrical object the rotation is known only up to multiplication by an element of the symmetry group. Such ambiguous…