Euclidean spaces are mathematical constructs that describe flat, two-dimensional or three-dimensional environments, where the familiar rules of geometry apply. Named after the ancient Greek mathematician Euclid, these spaces allow us to measure distances and angles using a coordinate system, typically represented by Cartesian coordinates. In a two-dimensional Euclidean space, points are defined by pairs of numbers (x, y), while in a three-dimensional Euclidean space, points are defined by triples (x, y, z). The properties of these spaces form the foundation for various fields, including physics, engineering, and computer graphics, enabling us to model and analyze real-world phenomena.