Changes

Introduction of coordinates by [[René Descartes]] and the concurrent development of [[algebra]] marked a new stage for geometry, since geometric figures, such as plane curves, could now be represented analytically, i.e., with functions and equations. This played a key role in the emergence of [[calculus]] in the seventeenth century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures. The subject of geometry was further enriched by the study of intrinsic structure of geometric objects that originated with [[Euler]] and [[Carl Friedrich Gauss|Gauss]] and led to the creation of topology and differential geometry.  

Introduction of coordinates by [[René Descartes]] and the concurrent development of [[algebra]] marked a new stage for geometry, since geometric figures, such as plane curves, could now be represented analytically, i.e., with functions and equations. This played a key role in the emergence of [[calculus]] in the seventeenth century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures. The subject of geometry was further enriched by the study of intrinsic structure of geometric objects that originated with [[Euler]] and [[Carl Friedrich Gauss|Gauss]] and led to the creation of topology and differential geometry.  

Since the nineteenth century discovery of non-Euclidean geometry, the concept of [[space]] has undergone a radical transformation. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean [[space]], which they only approximately resemble at small scales. These spaces may be endowed with additional [[structure]], allowing one to speak about length. Modern geometry has multiple strong bonds with [[physics]], exemplified by the ties between Riemannian geometry and [[general relativity]]. One of the youngest physical theories, [[string theory]], is also very geometric in nature.

Since the nineteenth century discovery of non-Euclidean geometry, the concept of [[space]] has undergone a radical transformation. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean [[space]], which they only approximately resemble at small scales. These spaces may be endowed with additional [[structure]], allowing one to speak about length. Modern geometry has multiple strong bonds with [[physics]], exemplified by the ties between Riemannian geometry and [[general relativity]]. One of the youngest physical theories, [[string theory]], is also very geometric in nature.