Perspective and projective geometry

✍ Scribed by Crannell, Annalisa; Frantz, Marc; Futamura, Fumiko

• Publisher: Princeton University Press
• Year: 2019
• Tongue: English
• Leaves: 291
• Category: Library

✦ Synopsis

Frontmatter -- Contents -- 0. Introduction and First Action -- 1. Window Taping -- 2. Drawing ART -- 3. What's the Image of a Line? -- 4. The Geometry of R2 and R3 -- 5. Extended Euclidean Space -- 6. Of Meshes and Maps -- 7. Desargues's Theorem -- 8. Collineations -- 9. Dynamic Cubes and Viewing Distance -- 10. Drawing Boxes and Cubes in Two-Point Perspective -- 11. Perspective by the Numbers -- 12. Coordinate Geometry -- 13. The Shape of Extended Space -- Appendix G. Introduction to GEOGEBRA -- Appendix R. Reference Manual -- Appendix W. Writing Mathematical Prose -- Acknowledgments -- Bibliography -- Index;Through a unique approach combining art and mathematics, Perspective and Projective Geometry introduces students to the ways that projective geometry applies to perspective art. Geometry, like mathematics as a whole, offers a useful and meaningful lens for understanding the visual world. Exploring pencil-and-paper drawings, photographs, Renaissance paintings, and GeoGebra constructions, this textbook equips students with the geometric tools for projecting a three-dimensional scene onto two dimensions. Organized as a series of exercise modules, students learn through hands-on inquiry and participation. Each lesson begins with a visual puzzle that can be investigated through geometry, followed by exercises that reinforce new concepts and hone students' analytical abilities. An instructor's manual available to teachers contains sample syllabi and advice, including suggestions for pacing and grading rubrics for art projects. Drawing vital interdisciplinary connections between art and science, Perspective and Projective Geometry is ideally suited for undergraduate students interested in mathematics or computer graphics, as well as for mathematically inclined students of architecture or art. · Features computer-based GeoGebra modules and hands-on exercises· Contains ample visual examples, math and art puzzles, and proofs with real-world applications· Suitable for college students majoring in mathematics, computer science, and fine art· Instructor's manual (available only to teachers)

✦ Table of Contents

Cover......Page 1
Contents......Page 6
0. Introduction and First Action......Page 12
1. Window Taping: The After Math......Page 20
Appendix: A Working Definition of n-Point Perspective......Page 33
2. Drawing ART......Page 36
3. What’s the Image of a Line?......Page 44
4.1 Euclidean Geometry: A Point of Comparison......Page 54
4.2 Euclidean Geometry Revisited: Similarities and Invariants......Page 62
5. Extended Euclidean Space: To Infinity and Beyond......Page 74
6. Of Meshes and Maps......Page 86
6.1 Field Trip: Perspective Poster......Page 98
7. Desargues’s Theorem......Page 102
7.1 Exploration and Discovery......Page 104
7.2 Working toward a Proof......Page 114
8. Collineations......Page 128
8.1 How Projective Geometry Functions......Page 130
8.2 Reflecting on Homologies and Harmonic Sets......Page 142
8.3 Elations (or, How to BeTransported in a Math Class)......Page 152
9. Dynamic Cubes and Viewing Distance......Page 156
10. Drawing Boxes and Cubes in Two-Point Perspective......Page 168
11. Perspective by the Numbers......Page 182
11.1 Discovering the Cross Ratio......Page 184
11.2 Eves’s Theorem......Page 200
11.3 An Angle on Perspective: Casey’s Theorem......Page 214
12. Coordinate Geometry......Page 222
12.1 Euclidean Geometry Enhanced with Algebra......Page 224
12.2 Introduction to Homogeneous Coordinates......Page 230
13. The Shape of Extended Space......Page 236
Appendix G. Introduction to GEOGEBRA......Page 246
Appendix R. Reference Manual......Page 256
Appendix W. Writing Mathematical Prose......Page 270
W.1.2 Mechanics and Conventions......Page 272
W.2 Pronouns and Active Voice......Page 274
W.3 Introducing and Using Variables, Constants, and Other Mathematical Symbols......Page 276
W.4 Punctuation with Algebraic Expressions in the Sentence......Page 278
W.5 Paragraphs and Lines......Page 280
W.6.2 Referring to Figures......Page 282
Acknowledgments......Page 284
Bibliography......Page 286
Index......Page 290

✦ Subjects

MATHEMATICS--Geometry--General;MATHEMATICS -- Geometry -- General