GeometryGeometry is probably the most accessible branch of mathematics, and can provide an easy route to understanding some of the more complex ideas that mathematics can present. This book is intended to introduce readers to the major geometrical topics taught at undergraduate level, in a manner that is both accessible and rigorous. The author uses world measurement as a synonym for geometry - hence the importance of numbers, coordinates and their manipulation - and has included over 300 exercises, with answers to most of them. The text includes such topics as: - Coordinates - Euclidean plane geometry - Complex numbers - Solid geometry - Conics and quadratic surfaces - Spherical geometry - Quaternions It is suitable for all undergraduate geometry courses, but it is also a useful resource for advanced sixth formers, research mathematicians, and those taking courses in physics, introductory astronomy and other science subjects. |
Contents
2 | 17 |
The Geometry of the Euclidean Plane | 63 |
The Geometry of Complex Numbers | 99 |
Solid Geometry | 137 |
Projective Geometry | 183 |
Conics and Quadric Surfaces | 211 |
30 | 229 |
38 | 236 |
48 | 244 |
Spherical Geometry | 253 |
Quaternions and Octonions | 287 |
305 | |
307 | |
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Common terms and phrases
algebra axes axis bisector called collinear complex numbers cone conic Consider corresponding cross ratio cube defined denote diagonal distance dodecahedron dual coordinates ellipse equal equation euclidean example Exercise Fano plane Find follows formula geometry given glide reflection horizon hyperbola integers intersection inversion isometry isosceles triangles latitude linear longitude matrix meet midpoint Möbius transformation multiplication nearest point nine-point circle non-zero notation nth roots octahedron octonions orthogonal pair parabola parallel perpendicular perspective polar pole polygon projective plane projective transformation Proof properties quadratic quadric surface quaternions radius real numbers right angles right-handed roots of unity rotary reflection rotation set of points Show sides solution space sphere square star stereographic projection symmetries tangent tetrahedron theorem triangle ABC unique unit vector product vertex vertices x-axis ZD₁ zero