Affine transformations of hyperbolic number plane

Öztürk, İskender; Özdemir, Mustafa

doi:10.1007/s40590-022-00455-2

Cited by 1 publication

(2 citation statements)

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“…The work by Öztürk and Özdemir [3] provides a more complete overview of the main issues of the classical theory of nonlinear birational transformations of the plane of threedimensional space. Dantas and Pan [4] considered Cremona quadratic transformations -the basics of the classical theory of nonlinear birational (cremonic) transformations of the plane of three-dimensional space.…”

Section: Introductionmentioning

confidence: 99%

“…In the above work [5], the conditions of transformation of the second-order surface and the plane were studied, and the properties of transformations were studied: for example, one and two-digit quadratic transformation having a bundle of direct carriers of the corresponding points. Öztürk and Özdemir [3] in their work gives a more complete survey of the basic questions of the classical theory of nonlinear birational transformations of the plane and three-dimensional space. This work is of great value because it contains the resolution of singularities of curves and surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Development and Definition of Biquadratic Transformations Using Spheres and Two-Way Hyperboloids

Baidabekov¹,

Kemelbekova²,

Kussebayev³

et al. 2022

MMEP

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The insufficient use of quadratic transformations in applied geometry is explained by the fact that the methods of quadratic transformations are not developed much, although dozens of works by leading experts in applied geometry are devoted to the study of this problem, the development of graphic models, and their application in applied geometry. The research is devoted to the development of the theory of definition of biquadratic transformations of the plane. The essence of the proposed method for modeling biquadratic transformations of the plane, generated by a binary mapping of two surfaces of the second order, facilitation and solution of complex problems of applied geometries. And also, by means of graphical models of biquadratic transformations of the plane to facilitate the construction of curves of the second and fourfold orders. Considering a combination of non-linear surfaces of the second order, obtain subgroups of biquadratic transformations of the plane. The developed algorithm will make it possible to determine mathematical models of canonical biquadratic transformations of the plane, which is necessary for their practical application.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%