Foundations Of Transcomplex Numbers:
An extension of the complex number system to four dimensions
By E. Pérez
Original copy deposited at U.S. Copyright Office.
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Foundations of transcomplex numbers is a mathematics book about a novel way of extending the complex numbers system to four-coordinate variables, maintaining the usual operations attributed to the complex numbers.
The book is typeset in high quality Latex format for superb equations and text readability, formatted for 8½ x 11 letter size printing. With 194 pages, generously illustrated with 51 illustrations, and many cross-references like:
- Table of Contents
- Index of Definitions
- Index of Figures
- Index of Nomenclature
- Index of Theorems
Seven chapters divided as follows:
- Ordered Pairs. The whole theory of transcomplex functions is based on the ordered pair concept: from the two-dimension plane up to the four-dimension space.
- Complex Numbers. The complex numbers system is derived from the ordered pairs concept.
- Transcomplex Numbers. Here starts the extension of the complex numbers into ordered pairs of complex numbers, arriving at the concept of transcomplexs.
- The Coordinate System S4. This chapter is devoted to deriving a suitable coordinate system to plot transcomplex functions.
- Transcomplex Functions. Functions of complex variables evolve to make space for functions of four-entries ordered pairs.
- Transcomplex Surfaces. A radical and totally new perception of surfaces generated by complex variables.
- Theorem Proofs. This chapter collects all the proofs of the theorems stated along the book.
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Some sample pages from the book
Fig. 1-2. Multiplication of ordered pairs
Fig. 1-4. The norm of an ordered pair
Fig. 2-4. The norm of a complex number
Fig. 2-5. The argument of a complex number
Fig. 4-10. The 4 subspaces of the hyperspace S4
Fig. 4-15. The cubicle number 4 of the hyperspace S4
Fig. 4-4. The real planes of the real cubicle.
Fig. 5-12. The the complex
trigonometric function W = sin Z
Fig. 5-16. The essence of the transcomplex maps