相关论文: The Conics Generated by the Method of Application …
Pythagoras' theorem, the area of a triangle as one half the base times the height, and Heron's formula are amongst the most important and useful results of ancient Greek geometry. Here we look at all three in a new and improved light, using…
This paper generalizes the notion of geometric curves such as hyperbolas and ellipses to more general vector spaces with an associated inner product. This is done by generalizing the definition in terms of loci and foci of said curves in…
In a previous paper we defined the circumconic of a triangle $ABC$ with respect to a point $P$ as the conic $\tilde C=T_{P'}^{-1}(N_{P'})$, where $N_{P'}$ is the $9$-point conic for the quadrangle $ABCP'$ with respect to the line at…
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…
Geometric sequences are found documented as early as 300BC in the text, Book IX of Elements written by Euclid of Alexandria. In this paper a new principle for identities involving the product of any k-number of terms of a geometric sequence…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
In this paper we construct a new class of algebraic surfaces in three-dimensional Euclidean space generated by a cyclic-harmonic curve and a congruence of circles. We study their properties and visualize them with the program Mathematica.
This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the…
We describe a geometric theory classified by Connes-Consani's epicylic topos and two related theories respectively classified by the cyclic topos and by the topos $[{\mathbb N}^{\ast}, \mathbf{Set}]$.
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…
At any point of a surface in the four-dimensional Euclidean space we consider the geometric configuration consisting of two figures: the tangent indicatrix, which is a conic in the tangent plane, and the normal curvature ellipse. We show…
The Circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of mathematical physics, optics and electricity. Here we discuss its…
This paper concentrates on the homogeneous (conformal) model of Euclidean space (Horosphere) with subspaces that intuitively correspond to Euclidean geometric objects in three dimensions. Mathematical details of the construction and…
One of the most important problems in Geometric Tomography is to establish properties of a given convex body if we know some properties over its sections or its projections. There are many interesting and deep results that provide…
The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
In this article, we study the geometry of plane curves obtained by three sections and another section given as their sum on certain rational elliptic surfaces. We make use of Mumford representations of semi-reduced divisors in order to…
In this work, we show how Euclidean 3-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…