The topological dimension of a Euclidean space equals its dimension. Smooth surfaces in Euclidean spaces are Riemann spaces. The quadratic integer rings are helpful to illustrate Euclidean domains. See also fixed points of isometry groups in Euclidean space. This led to modern abstract algebraic notions such as Euclidean domains. Points are considered fundamental objects in Euclidean geometry. There are two kinds of absolute geometry, Euclidean and hyperbolic. These are finite groups generated by reflections which act on a finite-dimensional Euclidean space. Two intersecting lines have the same properties as two intersecting lines in Euclidean geometry. A natural example comes from tangent bundles of smooth manifolds embedded in Euclidean space. Let be the group of the Euclidean isometries of a Euclidean space of dimension . This is analogous to the relationship between Euclidean geometry and non-Euclidean geometry. First, assume that there is a parametrization of by an open subset of Euclidean space. Mathematically, tessellations can be extended to spaces other than the Euclidean plane. Many of the other applications of the Euclidean algorithm carry over to Gaussian integers.