A crease pattern is an origami diagram that consists of all or most of the creases in the final model, rendered into one image. This is useful for diagramming complex and super-complex models, where the model is often not simple enough to diagram efficiently. The use of crease patterns originated with designers such as , who used them to record how their models were made. This allowed the more prolific designers to keep track of all their models, and soon crease patterns began to be used as a means for communication of ideas between designers. After a few years of this sort of use, designers such as Robert J. Lang, , Jun Maekawa and Peter Engel began to design using crease patterns. This allowed them to create with increasing levels of complexity, and the art of origami reached unprecedented levels of realism. Now most higher-level models are accompanied by crease patterns. Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams. For example, an algorithm for the automatic development of crease patterns for certain polyhedra with discrete rotational symmetry by composing right frusta has been implemented via a CAD program. The program allows users to specify a target polyhedron and generate a crease pattern that folds into it. Still, there are many cases in which designers wish to sequence the steps of their models but lack the means to design clear diagrams. Such origamists occasionally resort to the (SCP) which is a set of crease patterns showing the creases up to each respective fold. The SCP eliminates the need for diagramming programs or artistic ability while maintaining the step-by-step process for other folders to see. Another name for the sequenced crease pattern is the progressive crease pattern (PCP). (Wikipedia).
What are parallel lines and a transversal
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Patterns on Parallel Lines (2 of 2: Cointerior Angles on Parallel Lines)
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From playlist Angle Relationships
What are the Angle Relationships for Parallel Lines and a Transversal
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
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
Geometry - Identifying Consecutive Interior Angles from a Figure
π Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral
From playlist Parallel Lines and a Transversal
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
The Angles Created from Lines and a Transversal
π Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral
From playlist Parallel Lines and a Transversal
Lecture 3: Single-Vertex Crease Patterns
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 explores the local behavior of a crease pattern and characterizing flat-foldability of single-vertex crease patterns.
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 universal hinge patterns with the cube and maze gadget. NP-hardness problems involving partition and satis
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Class 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: Erik Demaine This class begins with a folding exercise and demonstration involving Origamizer. A high-level overview of the mathematical constr
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 hyperboloic paraboloid, hyparhedra, and the circular pleat. Topics include triangulated folding of the
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
The satisfying math of folding origami - Evan Zodl
Dig into the mathematical rules and patterns of folding origami, the ancient Japanese art of paper folding. -- Origami, which literally translates to βfolding paper,β is a Japanese practice dating back to at least the 17th century. In origami, a single, traditionally square sheet of pap
From playlist New TED-Ed Originals
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 definitions of origami terminology and a demonstration of mountain-valley folding. Turn, hide, color reve
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Proving Parallel Lines with Angle Relationships
π Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
Class 3: Single-Vertex Crease Patterns
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 algorithms for testing flat-foldability for a 1D MV pattern and for single-vertex MV pattern. An exercise walks
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Class 4: Efficient Origami Design
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 folded examples produced by TreeMaker and Origamizer. Explanation of the triangulation algorithm, checkerbo
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 several examples of box-pleating and maze-folding. Clarifications on NP-hardness are provided with a walkth
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
Labeling Alternate Interior Angles
π Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral
From playlist Parallel Lines and a Transversal
Lecture 5: Artistic Origami Design
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Jason Ku This lecture presents both the traditional and non-traditional style of origami with many visual examples. The lecture then moves onto
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012