Geometry: Springer Undergraduate Mathematics Series
Autor Roger Fennen Limba Engleză Paperback – 13 noi 2000
- 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.
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Specificații
ISBN-13: 9781852330583
ISBN-10: 1852330589
Pagini: 328
Ilustrații: XII, 313 p. 20 illus.
Dimensiuni: 178 x 235 x 17 mm
Greutate: 0.55 kg
Ediția:2001
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
ISBN-10: 1852330589
Pagini: 328
Ilustrații: XII, 313 p. 20 illus.
Dimensiuni: 178 x 235 x 17 mm
Greutate: 0.55 kg
Ediția:2001
Editura: SPRINGER LONDON
Colecția Springer
Seria Springer Undergraduate Mathematics Series
Locul publicării:London, United Kingdom
Public țintă
Lower undergraduateCuprins
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?.
Caracteristici
Adopts a unique approach - the more difficult sections are set in smaller type so that the reader can return to them after their second or third reading Introduces applications to astronomy