TL;DR
The paper introduces a unified, calculus-based model for various geometric spaces, enabling consistent calculations of distances, angles, and other properties across different geometries.
Contribution
It presents a novel uniform model that parametrizes different geometric spaces, facilitating calculations and theoretical analysis in a consistent framework.
Findings
Unified formulas for distances and angles across spaces
Easy computation of areas and volumes in various geometries
Detection of parallel and orthogonal properties in diverse spaces
Abstract
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of uniform equations among geometric spaces, uniform model applied to any space, which provides an easy way to calculate distances, plane and dihedral angles of any dimension, areas and volumes as well as parallel (where applied) and orthogonal property detection, study of not yet described spaces and more.
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Taxonomy
TopicsOptics and Image Analysis · Advanced Numerical Analysis Techniques · Geological Modeling and Analysis