Geometry, Paperback by Fenn, Roger, Brand New, Free shipping in the US

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Book Title
Geometry
ISBN
9781852330583
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Springer London, The Limited
ISBN-10
1852330589
ISBN-13
9781852330583
eBay Product ID (ePID)
1752206

Product Key Features

Number of Pages
Xii, 313 Pages
Language
English
Publication Name
Geometry
Subject
Geometry / General
Publication Year
2000
Type
Textbook
Author
Roger Fenn
Subject Area
Mathematics
Series
Springer Undergraduate Mathematics Ser.
Format
Trade Paperback

Dimensions

Item Height
0.3 in
Item Weight
40.9 Oz
Item Length
9.3 in
Item Width
7 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
00-044027
Dewey Edition
21
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
516
Table Of Content
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'.
Synopsis
Geometry 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, Geometry 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., 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.
LC Classification Number
QA440-699

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