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)

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Annalisa Crannell; Marc Frantz; Fumiko Futamura

Annalisa Crannell; Marc Frantz; Fumito Futamura

Princeton University, Department of Art & Archaeology

United States, United States of America

Princenton and Oxford, ©2019

Princeton, New Jersey, 2019

1, 2019

kolxo3 -- 95

lg2804730

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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, this book teaches students 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 electronic 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 mathematics, 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 art
· Electronic instructor's manual (available only to teachers)

"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."-- Site de l'éditeur

Cover......Page 1
PERSPECTIVE AND PROJECTIVE GEOMETRY......Page 5
Copyright......Page 6
Contents......Page 7
0 Introduction and First Action......Page 15
1 Window Taping.The After Math......Page 23
2 Drawing ART......Page 39
3 What’s the Image of a Line?......Page 47
4 The Geometry of R2 and R3......Page 55
5 Extended Euclidean Space. To Infinity and Beyond......Page 77
6 Of Meshes and Maps......Page 89
7 Desargues’s Theorem......Page 105
8 Collineations......Page 131
9 Dynamic Cubes and Viewing Distance......Page 159
10 Drawing Boxes and Cubes in Two-PointPerspective......Page 171
11 Perspective by the Numbers......Page 185
12 Coordinate Geometry......Page 225
13 The Shape of Extended Space......Page 239
Appendix GIntroduction to GEOGEBRA......Page 249
Appendix RReference Manual......Page 257
Appendix WWriting Mathematical Prose......Page 271
Acknowledgments......Page 285
Bibliography......Page 287
Index......Page 291

2020-10-11