Preface |
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xi | |
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1 | (8) |
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1 | (2) |
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3 | (6) |
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Problem Classification and Examples |
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9 | (8) |
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10 | (1) |
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11 | (6) |
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17 | (12) |
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General Algorithms and Upper Bounds |
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17 | (5) |
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22 | (7) |
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Planar Linkage Mechanisms |
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29 | (14) |
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29 | (2) |
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Kempe's Universality Theorem |
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31 | (9) |
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40 | (3) |
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43 | (16) |
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43 | (1) |
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43 | (1) |
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44 | (5) |
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49 | (4) |
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53 | (4) |
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57 | (2) |
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Reconfiguration of Chains |
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59 | (27) |
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Reconfiguration Permitting Intersection |
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59 | (8) |
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Reconfiguration in Confined Regions |
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67 | (3) |
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Reconfiguration Without Self-Crossing |
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70 | (16) |
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86 | (37) |
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86 | (1) |
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87 | (1) |
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88 | (4) |
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92 | (2) |
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94 | (2) |
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96 | (9) |
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Algorithms for Unlocking 2D Chains |
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105 | (8) |
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Infinitesimally Locked Linkages in 2D |
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113 | (6) |
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3D Polygons with a Simple Projection |
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119 | (4) |
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123 | (8) |
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125 | (1) |
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126 | (1) |
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127 | (4) |
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131 | (17) |
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131 | (12) |
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143 | (5) |
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148 | (19) |
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Producible Polygonal Protein Chains |
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148 | (6) |
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154 | (4) |
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158 | (9) |
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167 | (5) |
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167 | (1) |
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History of Origami Mathematics |
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168 | (1) |
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169 | (1) |
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170 | (2) |
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172 | (21) |
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Definitions: Getting Started |
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172 | (3) |
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Definitions: Folded States of 1D Paper |
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175 | (7) |
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Definitions: Folding Motions of 1D Paper |
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182 | (1) |
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Definitions: Folded States of 2D Paper |
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183 | (4) |
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Definitions: Folding Motions of 2D Paper |
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187 | (2) |
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189 | (4) |
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193 | (21) |
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One-Dimensional Flat Foldings |
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193 | (5) |
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Single-Vertex Crease Patterns |
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198 | (14) |
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Continuous Single-Vertex Foldability |
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212 | (2) |
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214 | (10) |
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Local Flat Foldability is Easy |
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214 | (3) |
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Global Flat Foldability is Hard |
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217 | (7) |
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224 | (8) |
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225 | (2) |
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Rectangular Maps: Reduction to 1D |
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227 | (1) |
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Hardness of Folding Orthogonal Polygons |
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228 | (2) |
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230 | (2) |
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Silhouettes and Gift Wrapping |
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232 | (8) |
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233 | (1) |
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Hamiltonian Triangulation |
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233 | (3) |
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236 | (1) |
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237 | (3) |
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240 | (14) |
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240 | (2) |
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242 | (1) |
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243 | (1) |
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244 | (2) |
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246 | (1) |
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247 | (2) |
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249 | (1) |
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250 | (4) |
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One Complete Straight Cut |
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254 | (25) |
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256 | (7) |
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263 | (16) |
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279 | (6) |
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Connection to Part III: Models of Folding |
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279 | (1) |
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Connection to Fold-and-Cut Problem |
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280 | (1) |
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Solution via Disk Packing |
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281 | (1) |
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Partial Solution via Straight Skeleton |
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281 | (4) |
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Geometric Constructibility |
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285 | (7) |
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285 | (1) |
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Huzita's Axioms and Hatori's Addition |
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285 | (3) |
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288 | (1) |
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289 | (1) |
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Generalizing the Axioms to Solve All Polynomials? |
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290 | (2) |
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Rigid Origami and Curved Creases |
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292 | (7) |
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292 | (1) |
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Curved Surface Approximation |
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293 | (3) |
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David Huffman's Curved-Folds Origami |
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296 | (3) |
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Introduction and Overview |
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299 | (7) |
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299 | (2) |
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301 | (3) |
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304 | (2) |
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Edge Unfolding of Polyhedra |
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306 | (33) |
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306 | (6) |
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Evidence for Edge Unfoldings |
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312 | (1) |
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Evidence against Edge Unfoldings |
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313 | (5) |
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318 | (3) |
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Special Classes of Edge-Unfoldable Polyhedra |
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321 | (12) |
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333 | (6) |
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Reconstruction of Polyhedra |
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339 | (19) |
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Cauchy's Rigidity Theorem |
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341 | (4) |
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345 | (3) |
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348 | (6) |
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354 | (4) |
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Shortest Paths and Geodesics |
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358 | (23) |
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358 | (4) |
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Shortest Paths Algorithms |
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362 | (4) |
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366 | (6) |
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Geodesics: Lyusternik--Schnirelmann |
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372 | (3) |
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375 | (6) |
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Folding Polygons to Polyhedra |
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381 | (56) |
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Folding Polygons: Preliminaries |
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381 | (5) |
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386 | (6) |
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392 | (4) |
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Exponential Number of Gluing Trees |
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396 | (3) |
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399 | (3) |
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The Foldings of the Latin Cross |
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402 | (9) |
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The Foldings of a Square to Convex Polyhedra |
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411 | (7) |
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Consequences and Conjectures |
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418 | (8) |
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426 | (3) |
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429 | (2) |
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431 | (6) |
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437 | (6) |
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437 | (1) |
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437 | (1) |
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438 | (5) |
Bibliography |
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443 | (18) |
Index |
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461 | |