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Geometry Roger Fenn

Geometry By Roger Fenn

Geometry by Roger Fenn

Reviews:
$16,49
Condition - Very Good
Only 1 left
Very Good

Summary

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.

Geometry Summary

Geometry by Roger Fenn

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?.

Additional information

GOR002489317
9781852330583
1852330589
Geometry by Roger Fenn
Roger Fenn
Springer Undergraduate Mathematics Series
Used - Very Good
Paperback
Springer London Ltd
2007-03-15
313
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in very good condition, but if you are not entirely satisfied please get in touch with us

Customer Reviews - Geometry