Preface

1 The Field ℝ⋆
1.1 Definition
1.2 An Order in ℝ⋆
1.3 Multiplicative Absolute Value
1.4 The Power Function
1.5 Multiplicative Trigonometric Functions
1.6 Multiplicative Inverse Trigonometric Functions
1.7 Multiplicative Hyperbolic Functions
1.8 Multiplicative Inverse Hyperbolic Functions
1.9 Multiplicative Matrices
1.10 Advanced Practical Problems
2 Multiplicative Plane Euclidean Geometry
2.1 The Multiplicative Vector Space ℝ⋆2
2.2 The Multiplicative Inner Product Space ℝ⋆2
2.3 The Multiplicative Euclidean Plane E⋆2
2.4 Multiplicative Lines
2.5 Multiplicative Orthonormal Pairs
2.6 Equations of a Multiplicative Line
2.7 Perpendicular Multiplicative Lines
2.8 Multiplicative Parallel Multiplicative Lines
2.9 Multiplicative Reflections
2.10 Multiplicative Congruence and Multiplicative Isometries
2.11 Multiplicative Translations
2.12 Multiplicative Rotations
2.13 Multiplicative Glide Reflections
2.14 Structure of the Multiplicative Isometry Group
2.15 Fixed Points and Fixed Multiplicative Lines
2.16 Advanced Practical Problems
3 Multiplicative Affine Transformations
3.1 Multiplicative Affine Transformations
3.2 Fixed Multiplicative Lines
3.3 The Fundamental Theorem
3.4 Multiplicative Affine Reflections
3.5 Multiplicative Shears
3.6 Multiplicative Dilatations
3.7 Multiplicative Similarities
3.8 Multiplicative Affine Symmetries
3.9 Multiplicative Rays and Multiplicative Angles
3.10 Multiplicative Rectilinear Figures
3.11 The Multiplicative Centroid
3.12 Multiplicative Symmetries of a Multiplicative Segment
3.13 Multiplicative Symmetries of a Multiplicative Angle
3.14 Multiplicative Barycentric Coordinates
3.15 Multiplicative Addition of Multiplicative Angles
3.16 Multiplicative Triangles
3.17 Multiplicative Symmetries of a Multiplicative Triangle
3.18 Congruence of Multiplicative Angles
3.19 Congruence Theorems for Multiplicative Triangles
3.20 Multiplicative Angle Sum of Multiplicative Triangles
3.21 Advanced Practical Problems
4 Finite Groups of Multiplicative Isometries of E⋆2
4.1 Cyclic and Dihedral Groups
4.2 Conjugate Subgroups
4.3 Orbits and Stabilizers
4.4 Regular Multiplicative Polygons
4.5 Similar Regular Multiplicative Polygons
4.6 Advanced Practical Problems
5 Multiplicative Geometry
5.1 The Space E⋆3
5.2 The Multiplicative Cross Product
5.3 Multiplicative Orthonormal Bases
5.4 Multiplicative Planes
5.5 Incidence Multiplicative Geometry
5.6 The Multiplicative Distance
5.7 Multiplicative Motions on S⋆2
5.8 Multiplicative Orthogonal Transformations
5.9 The Euler Theorem
5.10 Multiplicative Isometries
5.11 Multiplicative Segments
5.12 Multiplicative Rays
5.13 Multiplicative Spherical Trigonometry
5.14 A Multiplicative Congruence Theorem
5.15 Multiplicative Right Triangles
5.16 Advanced Practical Problems
6 The Projective Multiplicative Plane P⋆2
6.1 Definition Incidence Properties of P⋆2
6.2 Multiplicative Homogeneous Coordinates
6.3 The Desargues Theorem and the Pappus Theorem
6.4 The Projective Multiplicative Group
6.5 The Fundamental Theorem
6.6 Multiplicative Polarities
6.7 Multiplicative Cross Product
6.8 Advanced Practical Problems
7 The Multiplicative Distance Geometry on P⋆2
7.1 The Multiplicative Distance
7.2 Multiplicative Isometries
7.3 Multiplicative Motions
7.4 Elliptic Multiplicative Geometry
7.5 Advanced Practical Problems
8 The Hyperbolic Multiplicative Plane
8.1 Introduction
8.2 Definition of H⋆2
8.3 Multiplicative Perpendicular Lines
8.4 Multiplicative Distance of H⋆2
8.5 Multiplicative Isometries
8.6 Multiplicative Reflections of H⋆2
8.7 Multiplicative Motions
8.8 Multiplicative Reflections
8.9 Multiplicative Parallel Displacements
8.10 Multiplicative Translations
8.11 Multiplicative Glide Reflections
8.12 Multiplicative Angles
8.13 Advanced Practical Problems

Bibliography
Index