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Mathematics of paper folding

Index Mathematics of paper folding

The art of origami or paper folding has received a considerable amount of mathematical study. [1]

40 relations: Angle trisection, Art, Britney Gallivan, Compass-and-straightedge construction, Crease pattern, Crux Mathematicorum, Cut-the-Knot, Developable surface, Doubling the cube, Dragon curve, Equation, Erik Demaine, Flexagon, Fold-and-cut theorem, Gaussian curvature, Golden rectangle, Hexagon, Humiaki Huzita, Huzita–Hatori axioms, Involution (mathematics), Kawasaki's theorem, Kindergarten, Lill's method, Loss function, Maekawa's theorem, Map folding, Margherita Piazzola Beloch, Mathematics, Miura fold, Napkin folding problem, Neusis construction, NP-completeness, Origami, Pentagon, Regular paperfolding sequence, Rigid origami, Sheet metal, Silver ratio, Triangle, Wet-folding.

Angle trisection

Angle trisection is a classical problem of compass and straightedge constructions of ancient Greek mathematics.

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Art

Art is a diverse range of human activities in creating visual, auditory or performing artifacts (artworks), expressing the author's imaginative, conceptual idea, or technical skill, intended to be appreciated for their beauty or emotional power.

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Britney Gallivan

Britney Crystal Gallivan (born 1985) of Pomona, California, is best known for determining the maximum number of times that paper or other materials can be folded in half.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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Crease pattern

A crease pattern is an origami diagram that consists of all or most of the creases in the final model, rendered into one image.

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Crux Mathematicorum

Crux Mathematicorum is a scientific journal of mathematics published by the Canadian Mathematical Society.

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Cut-the-Knot

Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

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Developable surface

In mathematics, a developable surface (or torse: archaic) is a smooth surface with zero Gaussian curvature.

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Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem.

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Dragon curve

A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.

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Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

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Erik Demaine

Erik D. Demaine (born 28 February 1981) is a professor of Computer Science at the Massachusetts Institute of Technology and a former child prodigy.

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Flexagon

In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.

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Fold-and-cut theorem

The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut.

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.

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Golden rectangle

In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: \tfrac, which is 1:\varphi (the Greek letter phi), where \varphi is approximately 1.618.

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Hexagon

In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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Humiaki Huzita

Humiaki Huzita (藤田文章, Hepburn romanization: Fujita Fumiaki, 1924 – 26 March 2005) was a Japanese-Italian mathematician and origami artist.

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Huzita–Hatori axioms

The Huzita–Hatori axioms or Huzita–Justin axioms are a set of rules related to the mathematical principles of paper folding, describing the operations that can be made when folding a piece of paper.

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Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

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Kawasaki's theorem

Kawasaki's 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.

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Kindergarten

Kindergarten (from German, literally meaning 'garden for the children') is a preschool educational approach based on playing, singing, practical activities such as drawing, and social interaction as part of the transition from home to school.

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Lill's method

In mathematics, Lill's method is a visual method of finding the real roots of polynomials of any degree.

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Loss function

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

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Maekawa's theorem

Maekawa's theorem is a theorem in the mathematics of paper folding named after Jun Maekawa.

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Map folding

In the mathematics of paper folding, map folding and stamp folding are two problems of counting the number of ways that a piece of paper can be folded.

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Margherita Piazzola Beloch

Margherita Piazzolla Beloch (12 July 1879 in Frascati – 28 September 1976 in Rome) was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Miura fold

The is a method of folding a flat surface such as a sheet of paper into a smaller area.

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Napkin folding problem

The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter.

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Neusis construction

The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.

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NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

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Origami

) is the art of paper folding, which is often associated with Japanese culture.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Regular paperfolding sequence

In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite automatic sequence of 0s and 1s defined as the limit of the following process: At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence.

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Rigid origami

Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges.

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Sheet metal

Sheet metal is metal formed by an industrial process into thin, flat pieces.

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Silver ratio

In mathematics, two quantities are in the silver ratio (also silver mean or silver constant) if the ratio of the sum of the smaller and twice the larger of those quantities, to the larger quantity, is the same as the ratio of the larger one to the smaller one (see below).

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Triangle

A triangle is a polygon with three edges and three vertices.

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Wet-folding

Wet-folding is an origami technique developed by Akira Yoshizawa that employs water to dampen the paper so that it can be manipulated more easily.

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Redirects here:

Computational origami, Flat-foldability, Haga's theorem, Mathematical origami, Mathematics of origami, Origami math.

References

[1] https://en.wikipedia.org/wiki/Mathematics_of_paper_folding

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