Related papers: Solid angles in perspective
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
Building blocks and tiles are an excellent way of learning about geometry and mathematics in general. There are several versions of tiles that are either snapped together or connected with magnets that can be used to introduce topics like…
Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional…
Machine learning has found its way into almost every area of science and engineering, and we are only at the beginning of its exploration across fields. Being a popular, versatile and powerful framework, machine learning has proven most…
Both the basic educational contents for students and study programs for science teachers include several topics in physics and astronomy, from the simplest ones to others as advanced as nuclear fusion to explain stellar evolution and…
In this paper the problem of finding a normal form of triangles and plane quadrilaterals up to similarity is considered. Several normal forms for triangles and a normal form for quadrilaterals of special case are described. Normal forms of…
We discuss how the likely 2018 redefinition of the SI system of units might affect the ability of students to understand the link between the units and the new system. The likely redefinition will no longer define a set of base units, but…
On the basis of the data given in the works of different authors a criterion of phase-photometric method of measurement of energy angle of divergence has been formulated. Validity of application of the obtained relations for a ray beam with…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…
The progress of Particle Physics is closely linked to the progress in the understanding of the fundamental constants, like the finestructure constant, the mass of the electron or nucleon, or the electroweak mixing angle. The relation…
The IAU-1976 System of astronomical constants includes three astronomical units (i.e. for time, mass and length). This paper reports on the status of the astronomical unit of length (ua) and mass (MSun) within the context of the recent IAU…
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…
In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.
Let $I \subseteq \R$ be an open interval, $f : I \to \R$ a strictly positive function and denote by $\E^2$ the Euclidean plane. We classify all surfaces in the warped product manifold $I \times_f \E^2$ for which the unit normal makes a…
The article reviews some of the (fairly scattered) information available in the mathematical literature on the subject of angles in complex vector spaces. The following angles and their relations are considered: Euclidean, complex, and…
In this paper, we find all constant slope surfaces in the Euclidean 3-space, namely those surfaces for which the position vector of a point of the surface makes constant angle with the normal at the surface in that point. These surfaces…
In the paper by P. Quincey (2020) [1], the author claims that angles are not dimensionless quantities and that the radian should be a new independent base unit. However, the claim is not supported and the proposed redefinition will cause…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
Radius constants for several classes of analytic functions on the unit disk are obtained. These include the radius of starlikeness of a positive order, radius of parabolic starlikeness, radius of Bernoulli lemniscate starlikeness, and…