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. |