Perspective and Projective Geometry

Description

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) Cover PERSPECTIVE AND PROJECTIVE GEOMETRY Copyright Contents 0 Introduction and First Action 1 Window Taping. The After Math 2 Drawing ART 3 What’s the Image of a Line? 4 The Geometry of R2 and R3 5 Extended Euclidean Space. To Infinity and Beyond 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