Geometry (2nd Edition) – Complete Solutions Manual by Brannan, Esplen & Gray – PDF

ALL 7 CHAPTERS COVERED




SOLUTIONS MANUAL

, INSTRUCTORS’
MANUAL
for
Geometry
SECOND EDITION



D AV I D A . B R A N N A N
M AT T H E W F. E S P L E N
J E R E M Y J . G R AY




Geometry, 2nd Edition | Solutions for exercises
David A. Brannan, Matthew F. Esplen and Jeremy J. Gray | 
c The Open University, 2012

,
, Contents




1 Conics 1
1.1 Conic Sections and Conics 1
1.2 Properties of Conics 8
1.3 Recognizing Conics 17
1.4 Quadric Surfaces 32

2 Affine Geometry 49
2.1 Geometry and Transformations 49
2.2 Affine Transformations and Parallel Projections 52
2.3 Properties of Affine Transformations 56
2.4 Using the Fundamental Theorem of Affine Geometry 63
2.5 Affine Transformations and Conics 72

3 Projective Geometry: Lines 79
3.2 The Projective Plane RP2 79
3.3 Projective Transformations 83
3.4 Using the Fundamental Theorem of Projective Geometry 92
3.5 Cross-Ratio 93

4 Projective Geometry: Conics 100
4.1 Projective Conics 100
4.2 Tangents 102
4.3 Theorems 107
4.4 Applying Linear Algebra to Projective Conics 124

5 Inversive Geometry 128
5.1 Inversion 128
5.2 Extending the Plane 136
5.3 Inversive Geometry 142
5.4 Fundamental Theorem of Inversive Geometry 145
5.5 Coaxal Families of Circles 150


iii

Geometry, 2nd Edition | Solutions for exercises
David A. Brannan, Matthew F. Esplen and Jeremy J. Gray | 
c The Open University, 2012