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Viser: Geometry
Geometry
Roger Fenn
(2000)
Sprog: Engelsk
om ca. 15 hverdage
Detaljer om varen
- 1. Udgave
- Paperback
- Udgiver: Springer London, Limited (November 2000)
- ISBN: 9781852330583
- 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.
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 ".-
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 Desargues' 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 Pappus' 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 Observer's 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'.