Geometry of Generalized Complex Numbers

  title={Geometry of Generalized Complex Numbers},
  author={Anthony Harkin and Joseph B. Harkin},
  journal={Mathematics Magazine},
  pages={118 - 129}
Alternative definitions of the imaginary unit i other than i2 = −1 can give rise to interesting and useful complex number systems. The 16th-century Italian mathematicians G. Cardan (1501–1576) and R. Bombelli (1526–1572) are thought to be among the first to utilize the complex numbers we know today by calculating with a quantity whose square is −1. Since then, various people have modified the original definition of the product of complex numbers. The English geometer W. Clifford (1845–1879… 
In this study, we define a new non-commutative number system called hybrid numbers. This number system can be accepted as a generalization of the complex ( i = −1 ) , hyperbolic ( h = 1 ) and dual
Notions of Regularity for Functions of a Split-Quaternionic Variable
The utility and beauty of the theory holomorphic functions of a complex variable leads one to wonder whether analogous function theories exist for other (presumably higher dimensional) algebras. Over
Hybrid Complex Numbers: The Matrix Version
In this paper we review the notion of hybrid complex numbers, recently introduced to provide a comprehensive conceptual and formal framework to deal with circular, hyperbolic and dual complex. We
Generalized complex numbers over near-fields
Abstract The construction of the complex numbers over the reals has been generalized in many ways leading, amongs others, to the 2-dimensional elliptical complex numbers (= ordinary complex numbers),
Circle complexes and the discrete CKP equation
In the spirit of Klein's Erlangen Program, we investigate the geometric and algebraic structure of fundamental line complexes and the underlying privileged discrete integrable system for the minors
Fibonacci Elliptic Biquaternions
A. F. Horadam defined the complex Fibonacci numbers and Fibonacci quaternions in the middle of the 20th century. Half a century later, S. Hal{\i}c{\i} introduced the complex Fibonacci quaternions by
Clifford Fibrations and Possible Kinematics
Following Herranz and Santander (Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030) we will con- struct homogeneous spaces based on
Investigation of Generalized Hybrid Fibonacci Numbers and Their Properties
In \cite{Oz}, M. Ozdemir defined a new non-commutative number system called hybrid numbers. In this paper, we define the hybrid Fibonacci and Lucas numbers. This number system can be accepted as a
On the Construction of Generalized Bobillier Formula
In this study, we consider the generalized complex number system C_{p}={x+iy:x,y∈R,i²=p∈R} corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems
M ar 2 01 5 On the Construction of Generalised Bobillier Formula
In this paper, one-parameter planar motion in generalised complex plane (or p−complex plane) Cp = { x+ iy : x, y ∈ R, i = p } which is defined as a system of generalised complex numbers is studied.


Extending special relativity via the perplex numbers
In analogy to the complex numbers z=x+iy, where the ‘‘imaginary’’ i is such that i2=−1, a system of perplex numbers z=x+hy is introduced, where the ‘‘hallucinatory’’ h is such that ‖h‖=−1. This
Geometrie der Dynamen
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THE title of this book is somewhat misleading. Theobject of the first two parts is the discussion of certaingeometrical theorems. From these the laws for thecomposition of wrenches (Dynamen) can be
The screw calculus and its applications in mechanics
Abstract : The author sets forth the basic propositions of screw calculus on the basis of the elementary apparatus of modern vector algebra and indicates certain of its applications. The book sets
The Mathematical Papers
Eugene Wigner is above all a theoretical physicist. However he was one of the two men (Hermann Weyl was the other) who introduced a powerful new mathematical tool into quantum mechanics in its
Visual Complex Analysis
This chapter discusses Geometry and Complex Arithmetic, non-Euclidean Geometry*, Winding Numbers and Topology, and Vector Fields and Complex Integration.
Dual-Number Methods in Kinematics, Statics and Dynamics
The definition of co- Transformation Matrix Modeling of Joints and Links and its applications in Dual-Number Programming and Displacement Analysis are described.
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Kinematics, Statics and Dynamics
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Visual ComplexAnalysis
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