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Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations.
List of contents
Preface; 1. Parallel Folds; 2. V-Folds and Rotary Motion; 3. The Knight's Visor; 4. Pop-up Spinner; 5. Polyhedra: Rigid Origami and Flattening; 6. Algorithms for Pop-Up Design; 7. Pop-Up Design is Hard; 8. Solutions to Exercises.
About the author
Joseph O'Rourke is Olin Professor of Computer Science and Professor of Mathematics at Smith College. His research is in discrete and computational geometry, developing algorithms for geometric computations. He has won several awards, including a Guggenheim Fellowship in 1987 and the NSF Director's Award for Distinguished Teaching Scholars in 2001. He was named an ACM Fellow in 2012. He has published more than 165 papers, more than 30 of which were coauthored with undergraduates. He has taught folding and unfolding to students in grade school, middle school, high school, college and graduate school, and to teachers at all educational levels, as well as to researchers in mathematics and computer science. This is his seventh book.
Summary
The incredible 3-D dynamics of pop-up cards can be analyzed using high-school mathematics - a bit of trigonometry, but no calculus necessary. This book explores the beautifully intricate constructions, revealing a tangible, focused employment of mathematics in contrast to the often unmotivated presentation in traditional curricula.
