Paper folding | Mathematical theorems

Kawasaki's theorem

Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex that may be folded to form a flat figure. It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero.Crease patterns with more than one vertex do not obey such a simple criterion, and are NP-hard to fold. The theorem is named after one of its discoverers, Toshikazu Kawasaki. However, several others also contributed to its discovery, and it is sometimes called the Kawasaki–Justin theorem or Husimi's theorem after other contributors, Jacques Justin and Kôdi Husimi. (Wikipedia).

Kawasaki's theorem
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Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

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Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem

In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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The Second Fundamental Theorem of Calculus

This video introduces and provides some examples of how to apply the Second Fundamental Theorem of Calculus. Site: http://mathispower4u.com

From playlist The Second Fundamental Theorem of Calculus

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Kawasaki disease: diagnosis and treatment | Circulatory System and Disease | NCLEX-RN | Khan Academy

Kawasaki disease is diagnosed off the presence of symptoms rather than the results of tests. Symptoms include: conjunctivitis, rash, adenopathy, strawberry tongue, and rash on palms and soles of hands and feet. Four of these symptoms must be present, in addition to a fever which has lasted

From playlist Circulatory system diseases | NCLEX-RN | Khan Academy

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Calculus: The Fundamental Theorem of Calculus

This is the second of two videos discussing Section 5.3 from Briggs/Cochran Calculus. In this section, I discuss both parts of the Fundamental Theorem of Calculus. I briefly discuss why the theorem is true, and work through several examples applying the theorem.

From playlist Calculus

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Roland Bauerschmidt: Log-Sobolev inequality for the continuum Sine-Gordon model

The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations. Abstract: We derive a multiscale generalisation of the Bakry–Emery criterion for a measure to satisfy a Log-Sobolev inequality. Our criterion relies on the control of an

From playlist Workshop: Workshop: Singular SPDEs and Related Topics

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What is Kawasaki disease? | Circulatory System and Disease | NCLEX-RN | Khan Academy

Kawasaki disease (also known as mucocutaneous lymph node syndrome) is a type of vasculitis that affects medium arteries. Patients with Kawasaki disease can have symptoms like rashes on the palms of hands, soles of feet, in the eyes, and on the tongue (called strawberry tongue). Created by

From playlist Circulatory system diseases | NCLEX-RN | Khan Academy

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Convolution Theorem: Fourier Transforms

Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.

From playlist Partial differential equations

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Kids, Kawasaki Disease, and COVID-19: What Parents Should Know

While children are only a small minority of those who test positive for COVID-19, we’re starting to see evidence of a rare, but serious, complication in children that resembles a condition known as Kawasaki disease. Here’s what doctors say we should watch out for. Hosted by: Hank Green R

From playlist COVID-19 News & Updates

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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

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Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

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Roland Bauerschmidt: Lecture #3

This is a third lecture on "Log-Sobolev inequality and the renormalisation group" by Dr. Roland Bauerschmidt. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home

From playlist Summer School on PDE & Randomness

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Calculus - The Fundamental Theorem, Part 5

The Fundamental Theorem of Calculus. How an understanding of an incremental change in area helps lead to the fundamental theorem

From playlist Calculus - The Fundamental Theorem of Calculus

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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

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Viviani’s theorem

This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math​ #geometry #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwith

From playlist MathShorts

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Viviani's Theorem (visual proof via rotation)

This is a short, animated visual proof of Viviani's theorem, which states that the sum of the distances from any interior point to the sides of an equilateral triangle is equal to the length of the triangle's altitude. #math​ #geometry #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwith

From playlist Proofs Without Words

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What is the max and min of a horizontal line on a closed interval

👉 Learn how to find the extreme values of a function using the extreme value theorem. The extreme values of a function are the points/intervals where the graph is decreasing, increasing, or has an inflection point. A theorem which guarantees the existence of the maximum and minimum points

From playlist Extreme Value Theorem of Functions

Related pages

Kôdi Husimi | Empty sum | Maekawa's theorem | Bipartite graph | Vertex (geometry) | Mathematics of paper folding | Alternating series | Theorem | Rigid origami | Mathematical induction | Crease pattern | Dihedral angle