Let X and Y be normed real vector spaces. A mapping T: X Y is called preserving the distance r if for all x; y of X with kx ykX = r then kT(x) T(y)k = r. In this paper, we provide an overall account of the developmentof the Aleksandrov problem, especially the Aleksandrov Rassias problem for mappings which preserves distances with a noninteger ratioin in Hilbert spaces.