In mathematics, particularly differential geometry, a geodesic (/ˌdʒiːɵˈdiːzɨk/ JEE-o-DEE-zik or /ˌdʒiːɵˈdɛsɨk/ JEE-o-DES-ik) is a generalization of the notion of a "straight line" to "curved spaces". In the presence of an affine connection, a geodesic is defined to be a curve whose tangent vectors remain parallel if they are transported along it.