Differential calculus on the IR3(h) space

This study is about the deformation of coordinate functions on the 3-dimensional 3IR space and the geometry which will be identified on this space. The quantum 3d-space, defined by Manin and represented by 3qIR, is basically a deformation of the coordinate functions on q?3IR. It is obvious that, the algebra of coordinate functions on 3IR will be obtained by the limit as q goes to 1. () 1q? In this study, the 3qIR space has been taken into account and q?deformation has been transformed to deformation by defining a singular G matrix. As a technic term, we can call it as contraction . Although the structure obtained in the first step is a singular in the limit of , the singularity has disappointed since the using of algebraic structure of h?1q?3qIR. By this method, the relation of deformation have been reached. h? Then, by the help these new equalities, a differantial calculation has been made towards the space of deformation 3d quantum. h? Recently, by using qR matrix which provides the associativity of q?deformation algebra, a R matrix has been obtained for the h?deformation. Keywords: 3qIR space, 3hIR space, q?deformation, h?deformation.