Mathematical structures for spaces

Teacher(s)

Cherpion Marielle; Dos Santos Santana Forte Vaz Pedro;

Language

French

Main themes

1. Euclidean geometry and its generalizations. In particular curves (curvature, torsion, special curves), surfaces (curvatures, ruled surfaces), 3D objects (regular polyhedra, convex geometry, intersection of 3D objects) 2. The projective extension of euclidean geometry (projective space, projective transformations, duality, ...) 3. Introduction to other geometries : non-euclidean geometry and the axiom of parallels, topological classification of surfaces (Klein bottle, Euler characteristic, orientation), hyperbolic geometry (Escher paintings), ... 4. Forms and numbers in nature : the golden ratio and the Fibonacci numbers (properties, geometrical interest), fractals objects (constructions, fractal dimension)

Learning outcomes

At the end of this learning unit, the student is able to :
1	1) To describe a set of mathematical tools that enable the technical geometric calculations (lengths, areas, volumes, angles,...) 2) To help students to visualize, imagine and construct new spaces

Content

The different chapters of the course are:
- axiomatic geometry,
- affine geometry,
- euclidean geometry,
- polyhedra,
- quadrics,
- metric curve theory,
- metric theory of surfaces,
- tilings,
- fractal geometry.

Other information

LEPL1101, LEPL1102 and LEPL1105 or equivalent courses

Faculty or entity

> LOCI