Cover -- Preface -- Acknowledgement -- Notation -- Contents -- Chapter 1 Nbic Functions and Nbic Trigonometric Relations -- 1.1 Introduction -- 1.1.1 Circular Angle -- 1.1.2 Definition of Hyperbolic Angle and Tan-equivalent Hyperbolic (tehy) Angle -- 1.2 Definition and Interpretation of Nbic Angle -- 1.2.1 Nbic Angle and its Interpretation -- 1.2.2 Tan-Equivalent Nbic (teN) Angle -- 1.3 Symbolic Identification of Nbic Functions -- 1.3.1 Nbic Trigonometry -- 1.3.2 Interchangeability of Trigonometric and Hyperbolic Functions -- 1.3.3 Surface, Gaussian Curvature and Angle Sum -- 1.3.4 Nbic Functions and Nbic Trigonometric Relations -- 1.4 Complex Nbic Functions -- 1.4.1 Some Basic Complex Functions -- 1.4.2 Generation of Single Nbic Function, N (x, y) -- 1.4.3 Single Nbic Function With Suffixes A and B -- 1.4.4 Particular Case -- 1.4.5 Complex Single Nbic Function with Suffixes A and B, [NA / (x, x), NB / (x, x)] -- 1.5 Generation of Double Nbic Function,N2 (x,y) -- 1.5.1 As Generated from Complex Double Nbic Function, N2/(x, y) -- 1.5.2 Category 1 : (E type) -- 1.5.3 Particular Case -- 1.5.4 Category 2 : (F type) -- 1.5.5 Particular Case -- 1.5.6 Double Nbic Function with Suffixes A and B -- 1.6 Generation of Triple Nbic Function, N3(x, y) -- 1.6.1 As Generated from Complex Triple Nbic Function, N3 / (x, y) -- 1.6.2 Category 1 : (E type) -- 1.6.3 Particular Case -- 1.6.4 Category 2 : (F type) -- 1.6.5 Particular Case -- 1.6.6 Category M (Mixed Category) -- 1.6.7 Triple Nbic Function with Suffixes A and B -- 1.6.8 Particular Case -- 1.7 Definition and Development of Nbic Function -- 1.7.1 Single Nbic Function with Variable (x, y) : N(x, y) -- 1.7.2 Single Nbic Function with Variable of x Only : N(x, x) -- 1.7.3 Graphical Determination of Single Nbic Functions -- 1.7.4 Single Nbic Function with Complex Variable of (ix) Only : N (ix, ix).

1.7.5 Comparison with Corresponding Circular and Hyperbolic Functions -- 1.8 Derivation of Expressions of Other Basic Nbic Functions -- 1.8.1 To Find sinNx and cosNx, when only, tanNx is given -- 1.8.2 Differentiation Rule for Single Nbic Functions -- 1.8.3 Numerical Verification of Expressions -- 1.8.4 Basic Nbic Functions and their Derivatives -- 1.8.5 Integration Rule for Single Nbic Functions -- 1.8.6 Related Expressions Involving Differentiation and Integration -- 1.8.7 Interpretation and Representation in Terms of Circular Functions -- 1.9 Nbic Functions with Variable (2x, ± 2x) AND (2x, ± x) -- 1.9.1 Similarity of Forms -- 1.9.2 Single Nbic Function with Double Angle, N(2x, 2x) in Terms of, N(2x, x) -- 1.9.3 Some Examples Related to Nbic Functions with Variable (2x, ± 2x) and (2x, ± x) -- Chapter 2 Complex Nbic Function and Associated Topics -- 2.1 De Moivre's form Extended in Nbic Function -- 2.1.1 Complex Circular Function (Coci-function) -- 2.1.2 Complex Hyperbolic Function (Cohy-function) -- 2.1.3 Assessment of the Value of e and f, in Coci and Cohy-Functions -- 2.1.4 Value of the Parameter, e -- 2.1.5 Value of the Parameter, f -- 2.1.6 Alternative Formula for tanN(x, x) using Exponential and Fexponential Functions -- 2.1.7 Representation of Expansion for ch nx and sh nx -- 2.1.8 Representation of Expansion for, cos nx and sin nx -- 2.1.9 Few Products of Two Cohy 1 Functions when Compiled -- 2.1.10 Complex Single Nbic Functions (Cosn Function) -- 2.1.11 Checking of Expressions -- 2.1.12 Complex n Function (Con function) -- 2.2 Complex Number Systems -- 2.2.1 Complex Circular Number (Coci number) -- 2.2.2 Complex Hyperbolic Number (Cohy number) -- 2.2.3 Problems of Various Types of Complex Numbers in Terms of VariousTypes of Functions and Interrelations.

2.2.4 Relation Between Cosn Function, eiN / (x, y) = cosN(x, y) + i sinN(x, y),and the Product of Two Complex Numbers, z1 = a + i b and z2 = c + i d -- 2.2.5 Alternative Definition of Nbic Function (in terms of sin and cos) -- 2.2.6 Alternative Definition of Nbic Function (in terms of sinh and cosh) -- Chapter 3 Double Nbic Function, N2(x, y) -- 3.1 Categories of Double Nbic Function -- 3.1.1 Category 1: (E type) -- 3.1.2 Particular Case -- 3.1.3 Category 2: (F type) -- 3.1.4 Particular Case -- 3.1.5 Complex Double Nbic Function: N2e / (x, y) -- 3.2 Transfer of Double Nbic Function in Terms of Another Double Nbic Function or Single Nbic Function -- 3.2.1 For E1A and E2A type N2e(x, y) -- 3.2.2 Particular Case (E type) -- 3.2.3 For F1A and F2A type N2f (x, y) -- 3.2.4 Particular Case -- 3.2.5 Complex Double Nbic Function N2e / (x, x) as a Particular Case of N2e / (x, y) -- 3.2.6 Various tan-Formulas of Circular, Hyperbolic, Nbic Functions,in the Form of, tan(A + B) Formula, and Interrelations -- 3.2.7 Differentiation of Double Nbic Functions, N'2(x, x) -- 3.2.8 Complex Double Nbic Function Ratio, Rndn -- Chapter 4 Triple Nbic Function, N3 (x,y) -- 4.1 Triple Nbic Function, N3e(x, y) -- 4.1.1 Definition of Triple Nbic Function, N3e(x, y) -- 4.1.2 Particular Case, N3e(x, x) -- 4.1.3 Interchangeability of Third Order Nbic Functions -- 4.1.4 tanx in Terms of tanN3e(x), and tanN2f (x), through tan (A - B) Formula -- 4.1.5 Single Nbic Function N(x, x), in terms Triple Nbic Function N3e(x, x) -- 4.1.6 Similarities and Dissimilarities Between N2f (x) and N3e (x) Functions -- 4.1.7 Complex Triple Nbic Function Ratio, Rntn -- 4.1.8 Triple Nbic Function, N3f (x, y): -- 4.1.9 Particular Case -- Chapter 5 Reciprocal of Complex Nbic Functions -- 5.1 Various Types of Reciprocal of complex Nbic Functions -- 5.1.1 Particular Case.

5.1.2 Reciprocal of Complex Single Nbic Functions (Cosn Function), eiN/x = cosNx + i sinNx -- 5.1.3 Reciprocal of Complex Double Nbic Functions (Codn Function),eiN2/(x) = cosN2(x) + i sinN2(x) -- 5.1.4 Reciprocal of Complex n-Function (Con-Function), nix = sechx + i thx -- 5.1.5 Reciprocal of Complex Nbic Functions (General Procedure) -- Chapter 6 Circular Representation of Nbic functions (Nbic Circles) -- 6.1 Various Types of Nbic Circles -- 6.1.1 Circular Representation of Hyperbolic Functions -- 6.1.2 Circular Representation of Single Nbic Functions -- 6.1.3 Circular Representation of Double Nbic Functions (E type, F type) -- 6.1.4 Circular Representation of Triple Nbic Functions (E type, F type) -- 6.1.5 New Categorization for Circles -- Chapter 7 Application of Single Nbic Functions to Structural Problems -- 7.1 Application of Single Nbic Functions to Structural Problems [Beams on Elastic Foundation] -- 7.1.1 Basic Functions -- 7.1.2 Differentiation Rules -- 7.1.3 Beams on Elastic Foundation Equation -- 7.1.4 Solution Using Single Nbic Function -- Chapter 8 Matrix Representation of Nbic Functions -- 8.1 General -- 8.1.1 Types of Representations -- 8.1.2 Rotation -- 8.1.3 For Functions and Complex Functions -- 8.2 Trigonometric-Hyperbolic Interrelation of Nbic Functions -- Concluding Remarks -- Appendix A: Pythagorean Triplets with A Pair of Consecutive Numbers -- A-1 Introduction -- A-1.1 Separate Class of Pythagorean Triplets -- A-1.2 Proposed Method (Bairagi) -- A-2 Properties of These Number Chains -- A-2.1 v-Sequence -- A-2.2 u-Sequence -- A-2.3 x-Sequence -- A-2.4 y-Sequence -- A-2.5 z-Sequence -- A-3 Concluding Remarks -- Appendix B: Roots of Polynomial Equations-Application to the Resultants of Force Systems -- B-1 Introduction -- B-1.1 Analogous Representation of Like Parallel Force System.

B-1.2 Case 1: Polynomial Root Analogy of Like Parallel Force System -- B-1.3 Case 2: Polynomial Root Analogy of Unequal Parallel Force Systems -- B-2 Summary of Polynomial-Root Analogy -- Appendix C: Bairagi's Theorem on Trisection of an Angle -- C-1 Introduction -- C-1.1 Archimedean Model for Trisection of an Angle -- C-2 Bairagi's Model for Trisection of Angle -- C-2.1 Right Angled Triangle, where the Hypotenuse is Twice the Length of the Perpendicular -- C-2.2 Rhombus, in which Three Vertices are Equidistant from the Fourth Vertex -- C-3 Trapezium, in which Three Vertices are Equidistant From the Fourth Vertex -- C.4 Trisection of Arbitrary Angle-Use of Bairagi's Model -- Appendix D: Nbic Function Tables [Table 1 to Table 7] -- Table D-1 Trigonometric and Hyperbolic Functions of (x) -- Table D-2 Trigonometric and Hyperbolic Functions of (2x) -- Table D-3 Single Nbic Functions [N] of (x, x) and (X, -X) -- Table D-4 Double Nbic Functions [N2e ] of (x, x) -- Table D-5 Double Nbic Functions [N2f ] of (x, x) and (x,-x) -- Table D-6 Triple Nbic Functions [N3e ] of (x, x) -- Table D-7 Triple Nbic Functions [N3f ] of (x, x) -- Index.