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How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]]
| How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]] |
| Autore | O'Rourke Joseph |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
| Descrizione fisica | 1 online resource (xii, 177 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Soggetto topico |
Liaison theory (Mathematics)
Origami - Mathematics Polyhedra Protein folding |
| ISBN |
1-107-21769-5
1-139-23486-2 1-283-29846-5 1-139-12295-9 9786613298461 0-511-97502-3 1-139-11721-1 1-139-12787-X 1-139-11285-6 1-139-11504-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Part I. Linkages: 1. Robot arms; 2. Straight-line linkages and the pantograph; 3. Protein folding and pop-up cards; Part II. Origami: 4. Flat vertex folds; 5. Fold and one-cut; 6. The shopping bag theorem; Part III. Polyhedra: 7. Durer's problem: edge unfolding; 8. Unfolding orthogonal polyhedra; 9. Folding polygons to convex polyhedra; 10. Further reading; 11. Glossary; 12. Answers to exercises; 13. Permissions and acknowledgments. |
| Record Nr. | UNINA-9910458060203321 |
O'Rourke Joseph
|
||
| Cambridge : , : Cambridge University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]]
| How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]] |
| Autore | O'Rourke Joseph |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
| Descrizione fisica | 1 online resource (xii, 177 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Soggetto topico |
Liaison theory (Mathematics)
Origami - Mathematics Polyhedra Protein folding |
| ISBN |
1-107-21769-5
1-139-23486-2 1-283-29846-5 1-139-12295-9 9786613298461 0-511-97502-3 1-139-11721-1 1-139-12787-X 1-139-11285-6 1-139-11504-9 |
| Classificazione | MAT000000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Part I. Linkages: 1. Robot arms; 2. Straight-line linkages and the pantograph; 3. Protein folding and pop-up cards; Part II. Origami: 4. Flat vertex folds; 5. Fold and one-cut; 6. The shopping bag theorem; Part III. Polyhedra: 7. Durer's problem: edge unfolding; 8. Unfolding orthogonal polyhedra; 9. Folding polygons to convex polyhedra; 10. Further reading; 11. Glossary; 12. Answers to exercises; 13. Permissions and acknowledgments. |
| Record Nr. | UNINA-9910781991603321 |
|
O'Rourke Joseph
|
||
| Cambridge : , : Cambridge University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]]
| How to fold it : the mathematics of linkages, origami, and polyhedra / / Joseph O'Rourke [[electronic resource]] |
| Autore | O'Rourke Joseph |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2011 |
| Descrizione fisica | 1 online resource (xii, 177 pages) : digital, PDF file(s) |
| Disciplina | 516.3/5 |
| Soggetto topico |
Liaison theory (Mathematics)
Origami - Mathematics Polyhedra Protein folding |
| ISBN |
1-107-21769-5
1-139-23486-2 1-283-29846-5 1-139-12295-9 9786613298461 0-511-97502-3 1-139-11721-1 1-139-12787-X 1-139-11285-6 1-139-11504-9 |
| Classificazione | MAT000000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Machine generated contents note: Part I. Linkages: 1. Robot arms; 2. Straight-line linkages and the pantograph; 3. Protein folding and pop-up cards; Part II. Origami: 4. Flat vertex folds; 5. Fold and one-cut; 6. The shopping bag theorem; Part III. Polyhedra: 7. Durer's problem: edge unfolding; 8. Unfolding orthogonal polyhedra; 9. Folding polygons to convex polyhedra; 10. Further reading; 11. Glossary; 12. Answers to exercises; 13. Permissions and acknowledgments. |
| Record Nr. | UNINA-9910826034903321 |
|
O'Rourke Joseph
|
||
| Cambridge : , : Cambridge University Press, , 2011 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Reshaping Convex Polyhedra
| Reshaping Convex Polyhedra |
| Autore | O'Rourke Joseph |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Cham : , : Springer, , 2024 |
| Descrizione fisica | 1 online resource (245 pages) |
| Altri autori (Persone) | VîlcuCostin |
| ISBN | 3-031-47511-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Part I Tailoring for Every Body -- 1 Introduction to Part SPIlinkcolor100I -- 1.1 Convex Polyhedra: Background -- 1.2 Digon-Tailoring -- 1.3 Alexandrov's Gluing Theorem -- 1.4 Several Tailoring Examples -- 1.5 Summary of Part-I Results -- 2 Preliminaries -- 2.1 Geodesic Segments -- Quasigeodesics -- 2.2 Gauss-Bonnet Theorem -- 2.3 Cut Locus -- 2.3.1 Cut Locus: Definition and Properties -- 2.3.2 Star-Unfolding and Cut Locus -- 2.3.3 Fundamental Triangles -- 2.3.4 Cut Locus Partition -- 2.4 Cauchy's Arm Lemma -- 2.5 A Rigidity Result -- 2.6 Vertex-Merging -- 3 Domes and Pyramids -- 3.1 Domes -- 3.2 Cube/Tetrahedron Example -- 3.2.1 Slice → G-domes for Cube/Tetrahedron -- 3.3 Proof: G-dome → Pyramids -- 3.3.1 G-domes → Pyramids for Cube/Tetrahedron -- 4 Tailoring via Sculpting -- 4.1 Slice → G-domes -- 4.2 Pyramid → Tailoring -- 4.2.1 Notation -- 4.3 Sufficiently Close Truncations -- 4.3.1 Pyramid Case -- 4.3.2 General Case -- 4.4 Cube/Tetrahedron: Completion -- 4.4.1 Pyramid Removals -- 4.4.2 Pyramid Reductions by Tailoring -- 4.4.3 Seals -- 4.5 Hexagonal Pyramid Example -- 4.6 Tailoring Is Finer than Sculpting -- 5 Pyramid Seal Graph -- 5.1 Pyramid Digon Removal -- 5.1.1 Notation I -- 5.2 Cone Viewpoint -- 5.2.1 Notation II -- 5.3 Examples -- 5.4 Preliminary Lemmas -- 5.5 Pyramid Seal Graph Is a Tree -- 5.5.1 Other Digon Orderings -- 6 Algorithm for Tailoring via Sculpting -- 6.1 Algorithm 1: Slice → g-domes -- 6.1.1 Complexity of Sculpting -- 6.2 Algorithm 2: g-dome → Pyramids -- 6.3 Algorithm 3: Pyramid → Digons -- 6.4 Overall Tailoring Algorithm -- 7 Crests -- 7.1 Two Examples -- 7.2 Main Theorem and Supporting Lemmas -- 7.3 Algorithm 4: Pyramid → Crest -- 8 Tailoring via Flattening -- 8.1 Proof -- 8.1.1 Digon-Tailor P →Pflat -- 8.1.2 Vertex-Merge Q →Qflat -- 8.1.3 Scale Qflat →Qsflat -- 8.1.4 Trim Pflat →Psflat.
8.1.5 Reverse Psflat →Qt -- 8.1.6 Theorem: Tailoring via Flattening -- 8.2 Algorithm for Tailoring via Flattening -- 9 Applications of Tailoring -- 9.1 Enlarging and Reshaping -- 9.2 P-unfoldings -- 9.2.1 P-unfoldings and Reshaping -- 9.2.2 P-unfoldings and the WBG Theorem -- 9.3 Continuously Folding P onto Q -- Part II Vertex-Merging and Convexity -- 10 Introduction to Part SPIlinkcolor100II -- 10.1 Unfolding Convex Polyhedra -- 10.2 Part SPIlinkcolor100II Topics and Results -- 11 Vertex-Merging Reductions and Slit Graphs -- 11.1 Slit Graphs for Vertex-Mergings -- 11.2 Example: Reductions of Flat Hexagon -- 11.3 Example: Reductions of Cube -- 11.4 Example: Icosahedron -- 11.5 Example: Hexagonal Shape with Cycle -- 11.6 Vertex-Merging and Unfoldings -- 11.7 Unfolding Irreducible Surfaces -- 11.7.1 S: Doubly Covered Triangle -- 11.7.2 Net and Overlap -- 11.7.3 S: Isosceles Tetrahedron -- 12 Planar Spiral Slit Tree -- 12.1 Sequential Spiral Merge -- 12.2 Notation -- 12.3 Algorithm Description -- 12.4 Planar Proof -- 13 Convexity on Convex Polyhedra -- 13.1 Convex Curves -- 13.2 Notions of Convexity -- 13.3 Ag-Convexity -- 13.4 Geodesic Segments and Convex Sets -- 13.5 Relative Convexity -- 13.6 Convex Hull -- 13.7 Relative Convex Hull -- 13.8 Extreme Points -- 13.9 Relative Convex Hull of Vertices -- 13.10 Summary of Properties -- 13.10.1 Ag-Convexity -- 13.10.2 Geodesic Segments and Convex Sets -- 13.10.3 Relative Convexity -- 13.10.4 Convex-Hull Properties: conv(S) -- 13.10.5 Relative Convex Hull: rconv(S) -- 13.10.6 Extreme Points: ext(S) -- 13.10.7 Relative Convex Hull of Vertices -- 14 Minimal-Length Enclosing Polygon -- 14.1 Properties of the Minimal Enclosing Polygon -- 14.2 Shortening Algorithm -- 14.2.1 Curve-Shortening Flow -- 14.2.2 Algorithm Overview -- 14.2.3 Finding an Enclosing Geodesic Polygon -- 14.2.4 Algorithm for Curve-Shortening. 14.3 AG-Convexity and Z -- 14.4 Algorithm for rconv(V)= R(W) -- 15 Spiral Tree on Polyhedron -- 15.1 Notation -- 15.2 Icosahedron Example -- 15.3 Spiraling Algorithm for rconv -- 15.4 Proof: Slit Graph is a Tree -- 15.5 Spiraling Algorithm for Z(V)=min[V] -- 16 Unfoldings via Slit Trees -- 16.1 Notation -- 16.2 Unfoldings via Spiraling Algorithms -- 16.2.1 Two Cones -- 16.2.2 Reduction to Cylinder -- 16.2.3 Cube Example -- 16.2.4 Icosahedron Example -- 17 Vertices on Quasigeodesics -- 17.1 Notation -- 17.2 Quasigeodesics Through k Vertices -- 17.2.1 |V(Q)|=1 -- 17.2.2 |V(Q)|=2 -- 17.2.3 |V(Q)|=k, with 3k n -- 18 Conclusions and Open Problems -- 18.1 Part I -- 18.2 Part II -- Symbols -- References -- Index. |
| Record Nr. | UNINA-9910842293803321 |
|
O'Rourke Joseph
|
||
| Cham : , : Springer, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||