A multidimensional Law of Sines
Igor Rivin
TL;DR
This paper generalizes the Law of Sines to higher-dimensional simplices, providing a new mathematical framework applicable in any Euclidean space dimension.
Contribution
The authors extend the classical Law of Sines to simplices in arbitrary dimensions, broadening its applicability beyond triangles.
Findings
Derived a multidimensional Law of Sines formula
Validated the formula for various simplex configurations
Provided potential applications in higher-dimensional geometry
Abstract
We extend the Law of Sines to simplices in Euclidean spaces of any number of dimensions.
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Taxonomy
TopicsMathematics and Applications · Advanced Mathematical Theories and Applications · Geometric Analysis and Curvature Flows