Mathematical structures for spaces

licar1111  2023-2024  Louvain-la-Neuve

Mathematical structures for spaces
5.00 credits
30.0 h + 20.0 h
Q2
Teacher(s)
Buysse Martin; 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


Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Learning outcomes
Bachelor in Engineering : Architecture