 Euclidean space

Euclidean space is a fundamental concept in mathematics and geometry that describes a two-dimensional or higher-dimensional space where the familiar geometric and algebraic properties of Euclidean geometry apply. It is named after the ancient Greek mathematician Euclid, whose work laid the foundations for geometry. Here are some key characteristics of Euclidean space: 1. **Dimensions**: Euclidean space can exist in any number of dimensions. Commonly referenced dimensions include: - **1-dimensional**: A straight line (e.

${\mathbb{R}}^n$ with extra structure added to make it into a metric space.