Geometry
Author(s)
Bibliographic Information
Geometry
(Springer undergraduate mathematics series)
Springer, c2001
Available at 20 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Bibliography: p. 305-306
Includes index
Description and Table of Contents
Description
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.
Table of Contents
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 ".- 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?.
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