Mathematical structures for spaces
[FSAB1109]
[30h + 20h] 4 credits
This course is taught in the 1st semester.
Teacher(s): Pierre Bieliavsky(supplée Yves Félix), Yves Félix
Language: French
Level: First
Aims
2) To help students to visualize, imagine and construct new spaces
Main themes
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)
Content and teaching methods
- euclidean geometry
- affin geometry
- projective geometry
- metric curve theory
- metric theory of surfaces
- topology and surfaces
- fractal geometry
- axiomatic geometry
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
FSAB 1102 or an equivalent course