AU - Crasmareanu, M. TI - Quaternionic Product of Circles and Cycles and Octonionic Product for Pairs of Circles PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 17 VI - 1 IP - 1 4099 - http://ijmsi.ir/article-1-1418-en.html 4100 - http://ijmsi.ir/article-1-1418-en.pdf SO - IJMSI 1 ABĀ  - 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. CP - IRAN IN - Faculty of Mathematics, University "Al. I. Cuza", Iasi, 700506, Romania LG - eng PB - IJMSI PG - 227 PT - Research paper YR - 2022