Explore the fascinating geometry of Dihedrons and Quaternions in this 39-minute mathematics lecture. Delve into the rich mathematical structure of these algebras, comparing their similarities and differences. Discover how Dihedrons relate to 2x2 matrices and their fundamental quadratic form. Investigate the connections to relativistic geometry and generalized dot and cross products. Gain insights into the historical development of these concepts and their potential applications in modern mathematics and physics.