Euclidean Geometry definition?

Euclidean geometry is a mathematical system that describes the properties and relationships of points, lines, angles, surfaces, and solids in a flat, two-dimensional (plane) or three-dimensional (space) setting. It is based on the axioms and postulates introduced by the ancient Greek mathematician Euclid in his work "Elements," which laid the foundation for geometry as a formal discipline.

Key characteristics of Euclidean geometry include:

1. **Axioms and Postulates**: Euclidean geometry is built upon a set of axioms (statements accepted without proof) and postulates (self-evident truths) that define basic geometric concepts.

2. **Flat Space**: It assumes that the space is flat, meaning that it does not take into account the curvature of surfaces, which is a characteristic of non-Euclidean geometries (such as spherical or hyperbolic geometries).

3. **Geometric Figures**: It focuses on the study of geometric figures such as points, lines, triangles, circles, polygons, and other shapes, and explores their properties, congruence, similarity, and measurements.

4. **Theorems**: Many theorems are derived from the foundational axioms, such as the Pythagorean theorem, the properties of parallel lines, and the relationships between angles.

Overall, Euclidean geometry is fundamental in mathematics and is widely used in various fields, including engineering, physics, architecture, and computer graphics.