| Preface | p. vii |
| Symbols and notation | p. xvii |
| Introduction | p. 1 |
| Sense and nonsense | p. 1 |
| Geometric algebra | p. 2 |
| Products | p. 5 |
| Introduction | p. 5 |
| Real products | p. 5 |
| Complex products | p. 7 |
| Quaternion products | p. 8 |
| Summary | p. 11 |
| Vector Products | p. 13 |
| Introduction | p. 13 |
| The scalar product | p. 13 |
| The vector product | p. 14 |
| Dyadics | p. 16 |
| The outer product | p. 20 |
| Origins of the outer product | p. 20 |
| The geometric meaning of the outer product in 2D | p. 21 |
| The geometric meaning of the outer product in 3D | p. 25 |
| Summary | p. 32 |
| The Geometric Product | p. 33 |
| Introduction | p. 33 |
| Axioms | p. 33 |
| Redefining the inner and outer products | p. 37 |
| Blades | p. 41 |
| The geometric product of different vectors | p. 42 |
| Orthogonal vectors | p. 43 |
| Parallel vectors | p. 44 |
| Linearly independent vectors | p. 44 |
| Summary | p. 47 |
| Geometric Algebra | p. 49 |
| Introduction | p. 49 |
| Grades and pseudoscalars | p. 49 |
| Multivectors | p. 50 |
| Reversion | p. 53 |
| The inverse of a multivector | p. 54 |
| The imaginary properties of the outer product | p. 58 |
| The rotational properties of the 2D unit bivector | p. 59 |
| The imaginary properties of the 3D unit bivector and the trivector | p. 60 |
| Duality | p. 61 |
| Summary | p. 64 |
| Products in 2D | p. 65 |
| Introduction | p. 65 |
| The scalar-vector product | p. 66 |
| The scalar-bivector product | p. 67 |
| The vector-vector products | p. 67 |
| The inner product | p. 67 |
| The outer product | p. 69 |
| The geometric product | p. 70 |
| The vector-bivector product | p. 71 |
| The bivector-bivector product | p. 72 |
| Summary | p. 73 |
| Products in 3D | p. 75 |
| Introduction | p. 75 |
| The scalar-vector product | p. 75 |
| The scalar-bivector product | p. 76 |
| The scalar-trivector product | p. 77 |
| The vector-vector products | p. 77 |
| The inner product | p. 77 |
| The outer product | p. 79 |
| The geometric product | p. 80 |
| The vector-bivector product | p. 81 |
| The dyadic approach | p. 81 |
| The geometric approach | p. 84 |
| The vector-trivector products | p. 89 |
| The inner product | p. 89 |
| The outer product | p. 89 |
| The geometric product | p. 89 |
| The bivector-bivector products | p. 90 |
| The inner product | p. 91 |
| The outer products | p. 91 |
| The geometric products | p. 92 |
| The bivector-trivector products | p. 93 |
| The inner product | p. 93 |
| The trivector-trivector product | p. 94 |
| Product summary | p. 94 |
| Geometric algebra and the vector product | p. 97 |
| The relationship between the vector product and outer product | p. 97 |
| The relationship between quaternions and bivectors | p. 98 |
| The meet operation | p. 99 |
| Summary | p. 101 |
| Reflections and Rotations | p. 103 |
| Introduction | p. 103 |
| Reflections using normal vectors | p. 103 |
| Reflecting a vector in a mirror | p. 108 |
| Reflecting a bivector in a mirror | p. 109 |
| Reflecting a trivector in a mirror | p. 111 |
| Reflecting scalars | p. 112 |
| Rotations by reflections | p. 112 |
| Rotors | p. 117 |
| Rotating bivectors | p. 121 |
| Rotating trivectors | p. 123 |
| Rotating scalars | p. 124 |
| Rotors in exponential form | p. 124 |
| A rotor matrix | p. 125 |
| Building rotors | p. 128 |
| Interpolating rotors | p. 135 |
| Summary | p. 138 |
| Applied Geometric Algebra | p. 139 |
| Introduction | p. 139 |
| Sine rule | p. 139 |
| Cosine rule | p. 140 |
| Inscribed circle of a triangle | p. 141 |
| Circumscribed circle of a triangle | p. 143 |
| A point perpendicular to a point on a line | p. 147 |
| A point rotated an angle relative to a point on a line | p. 148 |
| Reflecting a vector about another vector | p. 150 |
| The position and distance of the nearest point on a line to a point | p. 152 |
| A line equidistant from two points | p. 155 |
| Intersection of two 2D lines | p. 156 |
| Intersection of two 2D lines using homogeneous coordinates | p. 160 |
| Orientation of a point and a 2D line | p. 162 |
| Intersection of a line and a circle | p. 163 |
| Orientation of a point with a plane | p. 165 |
| Plane equation | p. 166 |
| Orientation of a point with a convex object | p. 169 |
| Angle between a vector and a bivector | p. 172 |
| Angle between two bivectors | p. 173 |
| Intersection of a line and a plane | p. 175 |
| Intersection of a line and a sphere | p. 178 |
| Ray intersection and reflection | p. 180 |
| Summary | p. 182 |
| Conclusion | p. 183 |
| p. 185 |
| p. 187 |
| Bibliography | p. 191 |
| Index | p. 193 |
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