The trisector curve is transcendental
J. Monterde, F. Ongay
TL;DR
This paper proves that the distance trisector curve is transcendental, refuting previous conjectures that it was algebraic, and clarifies its mathematical nature.
Contribution
The paper establishes that the distance trisector curve is transcendental, providing a definitive answer to a longstanding conjecture in geometric curve theory.
Findings
The distance trisector curve is not algebraic.
It is proven to be transcendental.
This resolves a 2007 conjecture.
Abstract
We show that the distance trisector curve is not an algebraic curve, as was conjectured in the founding paper by T. Asano, J. Matousek and T. Tokoyama: "The distance trisector curve", Advances in Math., 212, 338-360 (2007).
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Computer Graphics and Visualization Techniques · Advanced Numerical Analysis Techniques