Geometry

With arithmetic, geometry is one of the earliest fields of mathematics. Geometry derives from the Ancient Greek words geo-, which means "earth," and metron, which means "measuring." Specifically, it is concerned with the qualities of space that are connected to the distance between figures, their form, size, and relative location in space. A geometer is a mathematician who specialises in geometry and works in the subject of geometrical analysis.

Geometry was nearly entirely committed to Euclidean geometry until the nineteenth century, which comprises the ideas of point, line and plane as well as the notions of distance, angle, surface and curve as its core concepts.

Several discoveries were made throughout the nineteenth century that significantly expanded the field of geometry. For example, Gauss' Theorema Egregium ("extraordinary theorem"), which states approximately that the Gaussian curvature of a surface is not reliant on any particular embedding in a Euclidean space, is among the earliest such findings. Thus, surfaces may be investigated intrinsically, i.e. as separate spaces, and this has been extended into the theory of manifolds and Riemannian geometry, among other areas.

Geometry, which was originally established to represent the physical world, now has applications in practically all disciplines, as well as in art, architecture, and other activities that are connected to graphics and computer graphics. Geometry has applications in a variety of disciplines of mathematics, even some that seem to be unrelated to geometry. For example, techniques of algebraic geometry are essential in Wiles's demonstration of Fermat's Last Theorem, a problem that was originally expressed in terms of simple arithmetic and that had remained unsolvable for many centuries before being discovered.