Ulianov Elliptical Transform: A New Paradigm for Ellipse Manipulation

Abstract

Policarpo Yoshin Ulianov

This paper introduces a groundbreaking advancement in the field of trigonometry: the development of Elliptical Trigonometry, a new area of mathematics founded on the Ulianov Elliptical Transform. By redefining traditional trigonometric functions to fit elliptical geometries, this research establishes a new framework for understanding and calculating angles, distances, and trajectories in elliptical shapes. These functions—elliptical cosine and sine—extend beyond the traditional applications, providing tools for more precise modeling in fields such as astrophysics, designer, and aerospace engineering. The potential impact of this discovery, akin to the historical significance of prime numbers and Boolean logic, opens new pathways in mathematical research and applied sciences.

Additionally, the paper explores the implications of the elliptical trigonometric functions in areas where standard trigonometric functions are currently applied, such as Fourier and Laplace transforms, and highlights the innovative nature of the elliptical arctangent function in analyzing orbital dynamics and collision probabilities. The Ulianov Elliptical Transform is demonstrated to provide both theoretical elegance and practical utility, suggesting its far-reaching effects across multiple disciplines. This transformative approach is expected to be the foundation for future developments in mathematics and technology, much like the introduction of prime numbers and Boolean logic in their respective fields.

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