Pictorial Calculus for Isometries

AbstractIn this paper a new graphical calculus for operating with isometries of low dimensional spaces is proposed. It generalizes a well-known graphical representation of vectors and translations in an affine space. Instead of arrows, we use arrows framed with affine subspaces at their end points. The head to tail addition of vectors and translations is generalized to head to tail composition rules for isometries. The material of this paper is elementary and can be used even in the framework of high-school geometry.