Mathematics of rigidity | Nonconvex polyhedra
In geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 such a polyhedron cannot be convex (this is also true in higher dimensions). The first examples of flexible polyhedra, now called Bricard octahedra, were discovered by Raoul Bricard. They are self-intersecting surfaces isometric to an octahedron. The first example of a flexible non-self-intersecting surface in , the Connelly sphere, was discovered by Robert Connelly. Steffen's polyhedron is another non-self-intersecting flexible polyhedron derived from Bricard's octahedra. (Wikipedia).
What is the difference between a regular and irregular polygon
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the definition of a regular polygon and how do you find the interior angles
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are the names of different types of polygons based on the number of sides
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between a regular and irregular polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What is the difference between convex and concave
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
What are four types of polygons
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Live CEOing Ep 186: Polyhedra in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Polyhedra in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
What is a polygon and what is a non example of a one
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture begins with a review of linkages and classifying graphs as generically rigid or flexible. Conditions for minimally ge
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Lecture 6: Architectural Origami
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Tomohiro Tachi This lecture presents Origamizer, freeform origami, and rigid origami applied to architectural and three-dimensional design cont
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture introduces the topics covered in the course and its motivation. Examples of applications are provided, types and char
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Lecture 16: Vertex & Orthogonal Unfolding
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture continues with open problems involving general unfoldings of polyhedra and proof of vertex unfolding using constructi
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Paul GUNNELLS - Cohomology of arithmetic groups and number theory: geometric, ... 3
In this lecture series, the first part will be dedicated to cohomology of arithmetic groups of lower ranks (e.g., Bianchi groups), their associated geometric models (mainly from hyperbolic geometry) and connexion to number theory. The second part will deal with higher rank groups, mainly
From playlist Γcole d'ΓtΓ© 2022 - Cohomology Geometry and Explicit Number Theory
Why is a doughnut equivalent to a mug? CHAPTERS: 00:00 - Turning a Mug into a Doughnut 01:30 - Geometry vs. Topology 02:05 - Review on Polyhedra 02:58 - Euler Characteristic of a Sphere 04:07 - Euler Characteristic of a Torus 04:51 - Euler Characteristic Formula given no. of Holes 05:10
From playlist Summer of Math Exposition 2 videos
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Ian Agol, Lecture 2: Finiteness of Arithmetic Hyperbolic Reflection Groups
24th Workshop in Geometric Topology, Calvin College, June 29, 2007
From playlist Ian Agol: 24th Workshop in Geometric Topology
Class 16: Vertex & Orthogonal Unfolding
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class reviews covers topologically convex vertex-ununfoldable cases and unfolding for orthogonal polyhedra, including the app
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This class begins with a folding exercise of numerical digits. Questions discussed cover strip folding in the context of efficienc
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
π Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons