Annual Member
| Author | Fenn, Roger. author |
|---|---|
| Title | Geometry [electronic resource] / by Roger Fenn |
| Imprint | London : Springer London : Imprint: Springer, 2001 |
| Connect to | http://dx.doi.org/10.1007/978-1-4471-0325-7 |
| Descript | XII, 313 p. online resource |
1. The Geometry of Numbers -- 1.1 Natural Numbers -- 1.2 Adding Natural Numbers -- 1.3 Multiplying Natural Numbers -- 1.4 Square and Triangular Numbers -- 1.5 Powers -- 1.6 Zero and Negative Numbers -- 1.7 Rational Numbers or Fractions -- 1.8 Powers of Rational Numbers -- 1.9 Rational Numbers as a Field -- 1.10 Real Numbers -- 1.11 Irrational Numbers -- 1.12 Four Famous Numbers: $$ \sqrt 2 $$ ?, ?, ? -- 2. Coordinate Geometry -- 2.1 Coordinates -- 2.2 ?nthe Space of Coordinates -- 2.3 The Line through Two Points -- 2.4 The Plane Containing Three Points -- 2.5 Distance and Angle -- 2.6 Polar Coordinates -- 2.7 Area -- 2.8 Hyperplanes -- 2.9 Angles between Hyperplanes and Nearest Points to Hyperplanes -- 3. The Geometry of the Euclidean Plane -- 3.1 The Life of Euclid โ -- 3.2 The Euclidean Axioms for the Plane -- 3.3 Angles and Lines -- 3.4 Some Basic Facts about Triangles -- 3.5 General Polygons -- 3.6 Congruences and Similarities -- 3.7 Isosceles Triangles -- 3.8 Circles -- 3.9 Triangles and their Centres -- 3.10 Metric Properties of Triangles -- 3.11 Three Surprising (and Beautiful) Theorems -- 4. The Geometry of Complex Numbers -- 4.1 What is $$ \sqrt { - 1} $$ -- 4.2 Modulus and Division -- 4.3 Unimodular Complex Numbers and the Unit Circle -- 4.4 Lines and Circles in the Complex Plane -- 4.5 Manipulating Complex Numbers -- 4.6 Infinity and the Riemann Sphere -- 4.7 Division and Inversion -- 4.8 Mobius Transformations -- 4.9 Cross Ratios -- 4.10 A Formula for the Cross Ratio -- 4.11 Roots of Unity -- 4.12 Formulre for the nth Roots of Unity -- 4.13 Solving Cubic and Biquadratic Polynomials -- 5. Solid Geometry -- 5.1 Points and Coordinates -- 5.2 Scalar Product -- 5.3 Cross Product -- 5.4 The Scalar Triple Product -- 5.5 The Vector Triple Product -- 5.6 Planes -- 5.7 Lines in Space -- 5.8 Isometries of Space -- 5.9 Projections -- 5.10 Polyhedra -- 6. Projective Geometry -- 6.1 The Projective Plane -- 6.2 Lines in the Projective Plane -- 6.3 Incidence and Duality -- 6.4 Desarguesโ Theorem -- 6.5 Cross Ratios Again -- 6.6 Cross Ratios and Duality -- 6.7 Projectivities and Perspectivities -- 6.8 Quadrilaterals -- 6.9 Projective Transformations -- 6.10 Fixed Points and Eigenvectors -- 6.11 Pappusโ Theorem -- 6.12 Perspective Drawing: Tricks of the Trade -- 6.13 The Fano Plane -- 7. Conics and Quadric Surfaces -- 7.1 Conic Sections -- 7.2 The Conic as Quadratic Curve -- 7.3 Focal Properties of Conics -- 7.4 The Motion of the Planets -- 7.5 Quadric Surfaces -- 7.6 The General Quadric Surface -- 8. Spherical Geonnetry -- 8.1 Geodesics -- 8.2 Geodesic Triangles -- 8.3 Latitude and Longitude -- 8.4 Compass Bearings -- 8.5 The Celestial Sphere -- 8.6 Observerโs Coordinates -- 8.7 Time and Right Ascension -- 9. Quaternions and Octonions -- 9.1 Extended Complex Numbers -- 9.2 Multiplying Quaternions -- 9.3 Inverses of Quaternions -- 9.4 Real and Pure Parts of Quaternions -- 9.5 Multiplying Quaternions and Linear Transformations of ?4 -- 9.6 Octonions -- 9.7 Vector Products in ?7 -- 9.8 Octonions and Associativity -- 9.9 Hexadecanions?
