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Modular Arithmetic
Published in Khaleel Ahmad, M. N. Doja, Nur Izura Udzir, Manu Pratap Singh, Emerging Security Algorithms and Techniques, 2019
Bézout’s theorem is defined as the description of algebraic geometry that states the number of common points, or intersection points, of two plane algebraic curves that do not share a common component (i.e., which do not have infinitely many common points) (Hefferon & Clark, 2003).
Polynomial Methods and Incidence Theory
Published in Technometrics, 2023
Chapter 2, Basic Real Algebraic Geometry in, is about the role of polynomial methods in incidence theory. It starts with a basic introduction to algebraic geometry over the set of real numbers. Chapter 3, Polynomial Partitioning, introduces the first polynomial method, studies the polynomial partitioning theorem, and shows how this theorem can be used to obtain incidence results in . Chapter 4, Basic Real Algebraic Geometry in is about the extension of results studied in the previous chapters.
On reconstruction of a matrix by its minors
Published in International Journal of Mathematical Education in Science and Technology, 2018
Azamat Akhtyamov, Meirav Amram, Artour Mouftakhov
In this paper, we formulate the conditions of existence of a matrix related to the given minors; these conditions are called Plücker relations. We propose a new approach to solving the problems of the reconstruction of a matrix, an approach that is different from the methods of projective geometry and algebraic geometry used previously. We use concepts of linear algebra methods without the involvement of the Grassmann algebra and the projective geometry [1,2]. The motivation for the results in this paper come from their application to some problems in mechanics, see [3–6].
Focusing attention on auxiliary lines when introduced into geometric problems
Published in International Journal of Mathematical Education in Science and Technology, 2019
The two problems in Figures 8 and 9 are united by the topic of angles. Auxiliary lines in both, in addition to a concretization of a definition (the straight angle and a circle), allow the transition to algebraic geometry (calculation of angles). Formerly scattered angles are united into one new entity (a straight angle in one case and an equilateral triangle in the other), focusing and structuring the learners’ attention accordingly.