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All Journal Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika
Laith H. M. Al-ossmi
College of Engineering, Thi-qar University, Al-Nasiriya city 370001, Iraq
Religion Education Mathematics Physics Other

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An elementary treatise on elliptic functions as trigonometry Laith H. M. Al-ossmi
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 5 No 1 (2023): Alifmatika - June
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35316/alifmatika.2023.v5i1.1-20

Abstract

This article concerns the examination of trigonometric identities from an elliptic perspective. The treatment of elliptic functions presented herein adheres to a structure analogous to the traditional exposition of trigonometric functions, with the exception that an ellipse replaces the unit circle. The degree of similarity between the elliptic functions and their trigonometric counterparts is moderated by the periodicity of the so-called El- functions. These identities not only establish the values of the functions, but also establish a correlation between their ratios and the major and minor axes of the underlying ellipse. The resemblance between the functions is somewhat modified by the periodic nature of the El-identities, whereby each ratio is associated with the major and minor axis of the ellipse. This article adopts the notation (E) to denote the El- functions and distinguish them from the opposite circular functions.
Cohen's kappa curves, new geometrical forms of dual curves Laith H. M. Al-ossmi; Imad Ibrahim Dawood
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 5 No 2 (2023): Alifmatika - December
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35316/alifmatika.2023.v5i2.226-246

Abstract

In this article, we introduce the concepts of taxicab and uniform products in the context of dual curves associated with Cohen's kappa, primarily defined by a set of inflection curvatures of an ellipse and a circle using parallel asymptotes. The novel curve under scrutiny, denominated as the "Like-Bulb Filament" (LBF) curve, is delineated as the locus of dual vertices originating from a couple of conic curvatures. The emergence of LBF transpires through the orchestrated arrangement of line segments emanating from a predetermined central focal point upon an elliptical form concomitant with a circular entity possessing a radius equivalent to the ellipse's minor axis. The LBF’s curve is intricately choreographed through the dynamic interplay of a constant unit circle and three asymptotic lines. Notably, two of these asymptotes achieve tangential intersections with the LBF curve, while the third gracefully traverses its central core. Additionally, we embark on a comprehensive algebraic examination complemented by a geometrically informed construction methodology. In these instances, a consistent conic curvature of the uint circle and an elliptical structure assume pivotal roles in the genesis of the LBF’s curve. Also, a geometric connection is speculated between these curve configurations and their relevance to engineering processes across fields. However, the document acknowledges the need for more intensive study on the presented traits. Hence, it emphasizes addressing the existing research gap in subsequent investigations.
Co-Authors Imad Ibrahim Dawood