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6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (MIT) 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (MIT)

Description

Includes audio/video content: AV lectures. This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. Acknowledgments Thanks to videographers Martin Demaine and Jayson Lynch. Includes audio/video content: AV lectures. This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. Acknowledgments Thanks to videographers Martin Demaine and Jayson Lynch.

Subjects

origami | origami | geometry | geometry | algorithm | algorithm | folding | folding | linkage | linkage | polyhedra | polyhedra | seam | seam | crease pattern | crease pattern | universal molecule | universal molecule | box pleating | box pleating | triangulation | triangulation | vertex | vertex | edge | edge | curved crease | curved crease | rigidity | rigidity | tensegrity | tensegrity | hinged dissection | hinged dissection | unfolding | unfolding | gluing | gluing | platonic solid | platonic solid | refolding | refolding | sculpture | sculpture | paper | paper | 3D chain | 3D chain | design | design

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT) 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT)

Description

Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions). Includes audio/video content: AV lectures. 6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Subjects

NP-completeness | NP-completeness | 3SAT | 3SAT | 3-partition | 3-partition | Hamiltonicity | Hamiltonicity | PSPACE | PSPACE | EXPTIME | EXPTIME | EXPSPACE | EXPSPACE | games | games | puzzles | puzzles | computation | computation | Tetris | Tetris | Nintendo | Nintendo | Super Mario Bros. | Super Mario Bros. | The Legend of Zelda | The Legend of Zelda | Metroid | Metroid | Pokémon | Pokémon | constraint logic | constraint logic | Sudoku | Sudoku | Nikoli | Nikoli | Chess | Chess | Go | Go | Othello | Othello | board games | board games | inapproximability | inapproximability | PCP theorem | PCP theorem | OPT-preserving reduction | OPT-preserving reduction | APX-hardness | APX-hardness | vertex cover | vertex cover | Set-cover hardness | Set-cover hardness | Group Steiner tree | Group Steiner tree | k-dense subgraph | k-dense subgraph | label cover | label cover | Unique Games Conjecture | Unique Games Conjecture | independent set | independent set | fixed-parameter intractability | fixed-parameter intractability | parameter-preserving reduction | parameter-preserving reduction | W hierarchy | W hierarchy | clique-hardness | clique-hardness | 3SUM-hardness | 3SUM-hardness | exponential time hypothesis | exponential time hypothesis | counting problems | counting problems | solution uniqueness | solution uniqueness | game theory | game theory | Existential theory of the reals | Existential theory of the reals | undecidability | undecidability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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Attribution

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6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs (MIT)

Description

6.890 Algorithmic Lower Bounds: Fun with Hardness Proofs is a class taking a practical approach to proving problems can't be solved efficiently (in polynomial time and assuming standard complexity-theoretic assumptions like P ≠ NP). The class focuses on reductions and techniques for proving problems are computationally hard for a variety of complexity classes. Along the way, the class will create many interesting gadgets, learn many hardness proof styles, explore the connection between games and computation, survey several important problems and complexity classes, and crush hopes and dreams (for fast optimal solutions).

Subjects

NP-completeness | 3SAT | 3-partition | Hamiltonicity | PSPACE | EXPTIME | EXPSPACE | games | puzzles | computation | Tetris | Nintendo | Super Mario Bros. | The Legend of Zelda | Metroid | mon | constraint logic | Sudoku | Nikoli | Chess | Go | Othello | board games | inapproximability | PCP theorem | OPT-preserving reduction | APX-hardness | vertex cover | Set-cover hardness | Group Steiner tree | k-dense subgraph | label cover | Unique Games Conjecture | independent set | fixed-parameter intractability | parameter-preserving reduction | W hierarchy | clique-hardness | 3SUM-hardness | exponential time hypothesis | counting problems | solution uniqueness | game theory | Existential theory of the reals | undecidability

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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https://ocw.mit.edu/rss/all/mit-allcourses.xml

Attribution

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6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (MIT)

Description

This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. Acknowledgments Thanks to videographers Martin Demaine and Jayson Lynch.

Subjects

origami | geometry | algorithm | folding | linkage | polyhedra | seam | crease pattern | universal molecule | box pleating | triangulation | vertex | edge | curved crease | rigidity | tensegrity | hinged dissection | unfolding | gluing | platonic solid | refolding | sculpture | paper | 3D chain | design

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

Site sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

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