# Réponse finale obtenue du bot:
response = « A fascinating exploration of geometric properties!
**Géométrie Euclidienne**
In Euclidean geometry, the properties of shapes and figures are based on the principles of points, lines, angles, and planes. Some key concepts include:
1. **Points**: A set of points is said to be « Euclidean » if it satisfies certain axioms, such as the parallel postulate.
2. **Lines**: Lines can be extended infinitely in both directions, and they have a fixed length.
3. **Angles**: Angles are formed by two rays sharing a common endpoint (vertex). Angles can be acute, obtuse, or straight.
4. **Planes**: A plane is a flat surface that extends infinitely in all directions.
**Géométrie Non-Euclidienne**
Non-Euclidean geometry is characterized by spaces with different properties from those of Euclidean geometry. Some examples include:
1. **Hyperbolic Geometry**: In hyperbolic space, the curvature is negative, and angles can be larger than 180°.
2. **Elliptical Geometry**: In elliptical space, the curvature is positive, and angles are less than 180°.
**Trigonométrie**
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. Key concepts include:
1. **Triangles**: A triangle is a polygon with three sides and three vertices.
2. **Angles**: Angles can be acute, obtuse, or straight.
3. **Sine, Cosine, and Tangent**: These trigonometric functions relate the ratios of the sides of a triangle.
**Topologie**
Topology is a branch of mathematics that studies the properties of shapes that are preserved under continuous deformations, such as stretching and bending. Key concepts include:
1. **Connectedness**: A space is said to be connected if it cannot be divided into two disjoint sets.
2. **Compactness**: A set is said to be compact if it is closed and bounded.
3. **Holes**: Topology studies the number of holes (or voids) in a shape.
Some examples of topological properties include:
* The torus (doughnut) has one hole.
* The sphere has no holes.
* The Möbius strip has one half-twist, creating an « inside » and an « outside ».
These are just a few examples of the fascinating world of geometric properties! »