Quaternions types and geometric applications

In this thesis, different types of quaternions and their geometric applications are examined. The study focuses on six types of quaternions: real, dual, split, hyperbolic, ellipsoidal, and commutative quaternions. The algebraic structures of each quaternion type are analyzed in detail, with emphasis on fundamental operations such as addition, subtraction, multiplication, scalar multiplication, conjugation, norm, and inverse. An interactive calculator was developed using GeoGebra software to allow users to perform these operations dynamically. Additionally, taking advantage of the ability of quaternions to represent motion and transformation in space, interpolation techniques were studied and visualized in the GeoGebra environment. This highlights the potential applications of quaternions in areas such as computer graphics, robotics, and animation. Through this study, the theoretical foundations of quaternion types are comparatively presented, and their simulations in GeoGebra provide both educational and practical contributions.