Related papers: Geometry of moving planes
This paper lays the foundations for a unified framework for numerically and computationally applying methods drawn from a range of currently distinct geometrical approaches to statistical modelling. In so doing, it extends information…
This paper gives an overview of several key innovations in the 19th century which led to complex geometry in the 20th century. This includes the creation of the complex plane, the work of Abel on addition theorems for generalized elliptic…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
The new great development in Physics could be related to the excited progress of a new mathematics: ternary theory of numbers, ternary Pithagor theorem and ternary complex analysis, ternary algebras and symmetries, ternary Clifford…
Jets frames, that is a generalisation of ordinary frames on a manifold, are described in a language similar to that of gauge theory. This is achieved by constructing the Cartan geometry of a manifold with respect to the diffeomorphism…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…
A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…
Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of f.
Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…
This paper sheds light on the essential characteristics of geodesics, which frequently occur in considerations from motion in Euclidean space. Focus is mainly on a method of obtaining them from the calculus of variations, and an explicit…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly…
Making a survey of recent constructions of universal cohomologies we suggest a new framework for a theory of motives in algebraic geometry.
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
The aim of the present text is twofold: to provide a compendium of Lagrangian and Hamiltonian geometries and to introduce and investigate new analytical Mechanics: Finslerian, Lagrangian and Hamiltonian. The fundamental equations (or…
In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…
This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the…