Explore the fascinating world of Dihedron algebra in this 32-minute video lecture from the "Famous Math Problems" series. Delve into the construction of true complex numbers through a precise and algebraic approach. Learn about the key role of the Dihedron algebra, a lesser-known sister to the Quaternion algebra, and discover its connection to 2x2 matrices over a field. Understand the origin of the name "Dihedron algebra" and its relation to finite group theory. Follow along as the lecture covers topics such as the algebra's basis, trace and determinant, symmetric bilinear form, adjugate, and conjugation. Gain valuable insights into this important mathematical concept and its place alongside other well-known algebraic structures.