TY - JOUR T1 - Quaternionic Product of Circles and Cycles and Octonionic Product for Pairs of Circles TT - JF - IJMSI JO - IJMSI VL - 17 IS - 1 UR - http://ijmsi.ir/article-1-1418-en.html Y1 - 2022 SP - 227 EP - 237 KW - Circle KW - Quaternion KW - Product KW - Octonion KW - Projective Geometry. N2 - 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. M3 10.52547/ijmsi.17.1.227 ER -