en عمومى General پژوهشي Research paper <span class="fontstyle0">This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given products are proposed.</span> Circle, Quaternion, Product, Octonion, Projective Geometry. 227 237 http://ijmsi.ir/browse.php?a_code=A-10-1642-1&slc_lang=en&sid=1 M. Crasmareanu mcrasm@uaic.ro 10031947532846009239 10031947532846009239 Yes Faculty of Mathematics, University "Al. I. Cuza", Iasi, 700506, Romania