This treatise investigates holomorphic functions defined on the space of bicomplex numbers introduced by Segre. The theory of these functions is associated with Fueter’s theory of regular, quaternionic functions. The algebras of quaternions and bicomplex numbers are developed by making use of so-called complex pairs. Special attention is paid to singular bicomplex numbers that lack an inverse. ...

In this paper, we give a beginners guide to the practicality of using dual-quaternions to represent the rotations and translations in character-based hierarchies. Quaternions have proven themselves in many fields of science and computing as providing an unambiguous, un-cumbersome, computationally efficient method of representing rotational information. We hope after reading this paper the reade...

1. A. F. Horadam. "Basic Properties of a Certain Generalized Sequence of Numbers." The Fibonacci Quarterly 3 (1965):161-75. 2. A. F. Horadam. "Complex Fibonacci Numbers and Fibonacci Quaternions." Amer. Math. Monthly 70 (1963):289-91. 3. A. L. Iakin. "Generalized Quaternions with Quaternion Components." The Fibonacci Quarterly 15 (1977):35Q-52. 4. A. L. Iakin. "Generalized Quaternions of Higher...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

All material objects perceivable by our sensations move in real 3D-space. In order to describe such movement in strict mathematical forms we need to realize, first, what does the space represent as a mathematical abstraction and how motion in it can be expressed? Isaac Newton had gave many cogitations with regard to categories of the space and time. Results of these cogitations have been devote...