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In the present book, a new form of trigonometric relations have been presented and discussed on adopting functions named as Nbic functions, created as the combination of circular and hyperbolic functions of several varieties by separating the real and imaginary parts of the product of complex circular and complex hyperbolic functions of simple or higher orders. Though the variations of the Nbic functions are Iimitless, the scope of the present book covers only Single, Double and Triple Nbic functions. Single Nbic functions, being the simplest of all the varieties, already are in extensive use in the solution of differential equations of fourth and eighth order, as the combinations of, sin-cosh, cos-sinh etc., which are often encountered in structural mechanics and elasticity problems.
The characteristics of the Nbic functions, and other various relations in the form of expressions and identities, written in the similar pattern of trigonometry, are presented and discussed systematically with critical remarks. That there exists a very close similarity in the structural pattern of the trigonometric relations of the Nbic functions with the corresponding ones of the year old circular functions and hyperbolic (or exponential) functions, has been established, and wherever possible, the interrelation among the Nbic and other ones are clearly brought into notice.
Circles when described through Nbic functions do not conform to our known Euclidean (full or complete) circles, and so also is the case with hyperbolic functions. Extending this knowledge, a completely new concept of categorizing of circles, has been proposed, and discussed in a full length chapter, in which the hyperbolic, Euclidean and Nbic circles, respectively, are grouped in the incomplete, complete and over complete category of circles.
A large number of typical numerical examples along with full length calculation is provided at the end of each chapter. This is intended to familiarize the details of the theoretical developments, and simultaneously to verify the correctness of the maiden theoretical formulations presented.
Related to the theoretical development of the text material, Appendices are suitably designed and provided at the end of the book. The solution of the problem of geometrical construction of trisection of a plane angle which remained unsolved by any mathematician of the world up till now, since the era of Archimedes, is fruitfully attempted, and is described and discussed on proposing Bairagi`s model, in Appendix C.isbn
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