Pop-Up Geometry: The Mathematics Behind Pop-Up Card

Description

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. 00 01.0_pp_i_iv_Frontmatter 02.0_pp_v_vi_Contents 03.0_pp_vii_x_Preface 04.0_pp_xi_xii_Acknowledgements 05.0_pp_1_14_Parallel_Folds 06.0_pp_15_30_V-Folds_and_Rotary_Motion 07.0_pp_31_46_The_Knights_Visor 08.0_pp_47_58_Pop-Up_Spinner 09.0_pp_59_84_Polyhedra_Rigid_Origami_and_Flattening 10.0_pp_85_100_Algorithms_for_Pop-Up_Design 11.0_pp_101_106_Pop-Up_Design_is_Hard 12.0_pp_107_120_Solutions_to_Exercises 13.0_pp_121_122_Symbols 14.0_pp_123_126_Bibliography 15.0_pp_127_130_Index