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Science & Math5642 Engineering4200 Mathematics2293 Social Sciences2143 Data Science, Analytics & Computer Technology2067 Physics1776 Computer Science1714 Humanities1550 Business & Management1463 Systems Engineering893 Literature861 Art, Design & Architecture797 Electrical Engineering797 Biology785 Chemistry696 Economics683 Energy, Climate & Sustainability658 Communication603 Health & Medicine586 AI564 Education & Teaching541 Algorithms and Data Structures493 Mechanical Engineering458 Materials Science and Engineering455 Software Design and Engineering449 Machine Learning427 Management421 Chemical Engineering366 Energy365 Policy and Administration347 Cognitive Science345 Operations334 Pedagogy and Curriculum331 Digital Learning328 Digital Business & IT326 History307 Media Studies306 Sociology304 Biomedical Technologies295 Earth Science278 Organizations & Leadership278 Urban Studies273 Visual Arts251 Programming & Coding250 Climate Science232 Biological Engineering207 Public Health205 Philosophy196 Innovation & Entrepreneurship185 Political Science185 Systems Thinking185 Educational Technology180 Psychology180 Adaptation and Resilience171 Anthropology171 Aerospace Engineering161 Finance & Accounting159 Language159 Architecture153 Game Design149 Climate and Energy Policy143 Strategy & Innovation143 Visualization143 Networks and Security142 Data Science138 Environmental Engineering129 Pathology and Pathophysiology124 Music121 Entrepreneurship118 Linguistics108 International Development104 Supply Chain96 Civil Engineering90 Nuclear Engineering88 Startups/New Enterprises86 Imaging71 Mental Health69 Faculty Leadership67 Ocean Engineering65 Gender Studies60 User Experience58 Environmental Design51 Immunology42 Built Environment41 Manufacturing35 Product Innovation35 Health Care Management34 Performing Arts34 Geography30 Marketing28 Sustainable Business28 Education Policy26 Innovation Process26 Law24 Real Estate24 Corporate Innovation22 Ecosystems22 Business Analytics21 Art History17 AR/VR/MR/XR12 Religion11 CyberSecurity6 Blockchain4 Natural Systems4 Negotiation & Communication4 Inventions & Patents3 Environmental and Climate Justice1 Innovation Ecosystems1

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MIT

Class 8: Fold & One Cut

Description: This lecture begins with a demonstration of software for fold and cut. Odd-degree vertices, and a comparison of skeleton method and tree method are discussed. Clarifications on the disk-packing method with a definition for the number of disks are given. Speaker: Erik Demaine

Gratis

MIT

Lecture 9: Pleat Folding

Description: This lecture introduces the hyperboloic paraboloid, hyparhedra, and the circular pleat. Topics include triangulated folding of the hypar, how paper folds between creases, and Gaussian curvature. Various proofs involving straight creases are given. Speaker: Erik Demaine

Gratis

MIT

Class 9: Pleat Folding

Description: This class covers creases in context of smoothness and a proof from the lecture involving Taylor expansion. Algorithms for the numbers of folding operations necessary for an MV string are presented. The class ends with a hypar folding exercise. Speaker: Erik Demaine

Gratis

MIT

Lecture 10: Kempe's Universality Theorem

Description: This lecture begins by defining folding motion by a series of folded state, linkages, graphs, and configuration space. A proof of Kempe’s universality theorem is presented along with Kempe’s gadgets, and also the Weierstrass approximation theorem. Speaker: Erik Demaine

Gratis

MIT

Class 10: Kempe's Universality Theorem

Description: This class presents open problems involving holes, sliding linkages, and generalizations of Kempe. A proof for the semi-algebraic sets for Kempe is presented and various origami axioms are given. The class ends with a continuation of hypar folding. Speaker: Erik Demaine

Gratis

MIT

Lecture 11: Rigidity Theory

Description: This lecture begins with a review of linkages and classifying graphs as generically rigid or flexible. Conditions for minimally generic rigid graphs are presented with degree-of-freedom analysis. Proofs of Henneberg and Laman characterizations are given. Speaker: Erik Demaine

Gratis

MIT

Class 11: Generic Rigidity

Description: This class covers how the pebble algorithm works with first a proof of the 2k property, and then 2k-3. Generic rigidity and the running time of the algorithm is discussed, and software simulations running the algorithm are shown. Speaker: Erik Demaine

Gratis

MIT

Lecture 12: Tensegrities & Carpenter's Rules

Description: This lecture covers infinitesimal rigidity and motion, and tensegrity systems as an extension of rigidity theory. The rigidity matrix, equilibrium stress, and duality are introduced, and a proof to Carpenter’s Rule Theorem is presented. Speaker: Erik Demaine

Gratis

MIT

Class 12: Tensegrities

Description: This class covers several examples of tensegrity structures and in Freeform software. A question on linear programming’s application to the motions and stresses is addressed. Speaker: Erik Demaine

Gratis

MIT

Lecture 13: Locked Linkages

Description: This lecture explores algorithms for unfolding 2D chains including ODE, pointed pseudotriangulations, and the energy method. Locking rules are then extrapolated to address Spherical Carpenter’s Rule, infinitesimally locked linkages, and locked 3D chains. Speaker: Erik Demaine

Gratis

MIT

Class 13: Locked Linkages

Description: This class reviews Carpenter’s Rule and properties of pseudotriangulation. Various proofs are presented, which cover topics including non-zero stresses, linear and equilateral locked trees, and unfolding of 4D chains. Speaker: Erik Demaine

Gratis

MIT

Class 14: Hinged Dissections

Description: This class focuses on hinged dissections. Examples of hinged dissections and several built, reconfigurable applications are offered Pseudopolynomials, triangulation, and 3D dissections are then discussed. Speaker: Erik Demaine

Gratis

MIT

Lecture 15: General & Edge Unfolding

Description: This lecture begins with describing polyhedron unfolding for convex and nonconvex polygons. Algorithms for shortest path solutions and unfoldings are presented along with how to determine whether an edge unfolding exists. Speaker: Erik Demaine

Gratis

MIT

Class 15: General & Edge Unfolding

Description: This class begins with defining handles and holes, and the Gauss-Bonnet Theorem applied to convex polyhedra. Algorithms for zipper unfolding, edge ununfoldable polyhedra, square-packing, band unfolding, and blooming of convex polyhedra are presented. Speaker: Erik Demaine

Gratis

MIT

Lecture 16: Vertex & Orthogonal Unfolding

Description: This lecture continues with open problems involving general unfoldings of polyhedra and proof of vertex unfolding using construction of facet-paths. Approaches for unfolding orthogonal polyhedra, grid unfolding, and folding convex polyhedra are presented. Speaker: Erik Demaine

Gratis

MIT

Class 16: Vertex & Orthogonal Unfolding

Description: This class reviews covers topologically convex vertex-ununfoldable cases and unfolding for orthogonal polyhedra, including the approach of heavy-light decomposition. The class also reviews Cauchy’s Rigidity Theorem. Speaker: Erik Demaine

Gratis

MIT

Lecture 17: Alexandrov's Theorem

Description: This lecture addresses the mathematical approaches for solving the decision problem for folding polyhedra. A proof of Alexandrov’s Theorem and later a constructive version of Alexandrov is presented. Gluing trees and rolling belts are introduced. Speaker: Erik Demaine

Gratis

MIT

Class 17: D-Forms

Description: This class introduces the pita form and Alexandrov-Pogorelov Theorem. D-forms are discussed with a construction exercise, followed by a proof that D-form surfaces are smooth and are the convex hull of the seam. Rolling belts are addressed at the end. Speaker: Erik Demaine

Gratis

MIT

Lecture 18: Gluing Algorithms

Description: This lecture begins how to construct a gluing tree. Combinatorial bounds and algorithms are proved for gluing results, which include the general case, edge-to-edge, and bounded sharpness. The different gluings for the cross are also shown. Speaker: Erik Demaine

Gratis

MIT

Lecture 19: Refolding & Smooth Folding

Description: This lecture begins with a problem involving unfolding and refolding. Examples of smooth foldings and unfoldings are given, followed by a problem involving the wrapping of a sphere and a proof that the wrappings are contractive. Speaker: Erik Demaine

Gratis

MIT

Class 19: Refolding & Kinetic Sculpture

Description: This class first covers research findings involving common unfoldings of boxes. Several examples of kinetic sculptures and machines are shown, including Theo Jansen’s Strandbeests and Arthur Ganson’s works at the MIT Museum. Speaker: Erik Demaine

Gratis

MIT

Lecture 20: Protein Chains

Description: This lecture focuses on the folding of the backbone chain of proteins in relation to fixed-angle linkages. Four problems types (span, flattening, flat-state connectivity, locked) are presented, followed by the canonicalization of a producible chain. Speaker: Erik Demaine

Gratis

MIT

Class 20: 3D Linkage Folding

Description: This class introduces recent research on flattening fixed-angle chains and addresses flipping of pockets in a polygon. Flaws and omissions in proofs on a bounding number of flips are presented along with a correct version of Bing and Kazarinoff’s proof. Speaker: Erik Demaine

Gratis

MIT

Lecture 21: HP Model & Interlocked Chains

Description: This lecture presents the hydrophobicity (HP) model for protein folding and optimization using parity cases. Interlocked 3D chains are presented through a table depicting different cases for combinations of open and closed chains. Speaker: Erik Demaine

Gratis

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4200

Mathematics2293

Social Sciences2143

Data Science, Analytics & Computer Technology2067

Physics1776

Computer Science1714

Humanities1550

Business & Management1463

Systems Engineering893

Literature861

Art, Design & Architecture797

Electrical Engineering797

Biology785

Chemistry696

Economics683

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Får jeg et diplom eller certifikat?

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