Branch of mathematics originally concerned with the study of metric relations between points, lines, curves, surfaces, and volumes of three-dimensional space and mainly with the measurements of geometric figures.

More recently, the focus in geometry has been on geometric space figures and on their properties that remain invariant under certain transformations.

### Subdivisions

**Analytic geometry**is a branch of geometry that originated in René Descartes and Pierre de Fermat’s works, in which figures are represented in \(\mathbb{R}^{2}\) or \(\mathbb{R}^{3}\), that is, in a space with a two-dimensional or three-dimensional Cartesian coordinate system. Therefore, in analytic geometry, geometry problems are solved using algebraic calculation tools.**Solid geometry**is the branch of geometry concerned with the relative positions of plane figures and three-dimensional figures.**Descriptive geometry**is the branch of geometry concerned with the orthogonal projections of space figures onto two perpendicular planes.**Plane geometry**is the branch of geometry concerned with figures constructed on a same plane. The frame of reference for plane geometry is the geometric plane.**Projective geometry**is the branch of geometry concerned with the intuitive concepts of perspective and horizon. It deals with the properties of figures that are invariant under central projections with one, two or three vanishing points.

### Etymological note

The term “geometry” is derived from the Greek γεωμέτρης (geōmétrēs), meaning “geometer” or “land-surveyor,” and from γῆ (gê), meaning “earth” and μέτρον (metron) meaning “measurement.” Therefore, it is “the science of measuring land.”