Non-Euclidean geometry is a branch of geometry that deals with Euclid’s fifth postulate—the “parallel postulate” that only one line is parallel to a given line through a given external point. This postulate is replaced by one of two alternative postulates. The results of these two alternative types of non-Euclidean geometry are similar to those in Euclidean geometry, except for those propositions involving explicit or implicit parallel lines. (For more information about non-Euclidean geometry, see “History of Mathematics.”)