Lecture

Frenet-Serret Formulas: Curvature and Torsion

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In course

MATH-213: Differential geometry I - curves and surfaces

This course serves as an introduction to classical differential geometry, which studies the geometric properties of curves and surfaces in the Euclidean space. ...

Description

This lecture covers the Frenet-Serret formulas in the context of curvature and torsion, explaining the concepts of the Freret frame, Serret frame, and the Frenet coordinate system. It delves into the definitions and properties of curvature and torsion, illustrating how they are calculated and their geometric interpretations. The lecture also discusses the regularity conditions for curves in three-dimensional space, providing insights into the relationships between curvature, torsion, and the Frenet frame.

Instructor

Marc Troyanov

Expertise Differential Geometry Geometric Analysis Teaching & PhD Past EPFL PhD Students Olivier Mermoud, Khaled Gafaiti, Serguei Timochine, Stephen Ducret, Ratiba Djelid, Zahra Sinaei, Luc Genton, Adrien Giuliano Marcone, Guillaume Buro, Bruno Luiz Santos Correia Courses Advanced linear algebra II MATH-115(b) The purpose of this course is to introduce some basic notions of linear algebra and to rigorously prove the main results in the field.

Official source

Ontological neighbourhood

Mathematics

Geometry: Differential geometry

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