Rigid Motions, Reflections And Groups

Rigid motion is a transformation consisting of some rotations andtranslations operation which leave a given shape or arrangementunchanged. In other words, a rigid motion of a shape is a way of movingthe shape without bending tearing or distorting it, so that it looks thesame. Reflectiorl on the other hand, is the operation ofexchanging allpoints of a mathematical object with their mirror images (i.e., reflectionsin a minor).This paper is aimed to discuss the set of rigid motion and reflection ofsome shapes, together with the operation of compositions which form agroup, called the group of s;rmmetries, of the shape. The operation ofcompositions is commonly written in usual order, (for example, if rmeans rotation, and ft reflects about horizontal axis-ft, then the operationur o h" means we do rigid motion Ir first, followed by r). This paper alsoshows that the rigid motion can be wrifien as permutation, but not allpermutations are rigid motion