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The toric sections: a simple introduction

2017/08/01 by Luca Moroni, Moroni, Luca · 1 citation
Computer Science · Mathematics · #97G40 #FOS: Mathematics #Geometric and Algebraic Topology #History and Overview (math.HO) #Mathematics and Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1708.00803

openalex publication_date 2017/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review, from a didactic point of view, the definition of a toric section and the different shapes it can take. We'll then discuss some properties of this curve, investigate its analogies and differences with the most renowned conic section and show how to build its general quartic equation. A curious and unexpected result was to find that, with some algebraic manipulation, a toric section can also be obtained as the intersection of a cylinder with a cone. Finally we'll show how it is possible to construct and represent toric sections in the 3D Graphics view of Geogebra. In the article only elementary algebra is used, and the requirements to follow it are just some notion of goniometry and of tridimensional analytic geometry.

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