Questions tagged [origami]

In modern usage, the word "origami" is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal of is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques.

Origami (折り紙), from ori meaning "folding", and kami meaning "paper" (kami changes to gami due to rendaku) is the art of paper folding, which is often associated with Japanese culture. In modern usage, the word "origami" is used as an inclusive term for all folding practices, regardless of their culture of origin. The goal of is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques (Wikipedia).

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How well-studied is origami field theory?

It's well known that angle trisection cannot be done with straightedge and compass alone, as Theorem 1. If $z \in \mathbb C$ is constructible with straightedge and compass from $\mathbb Q$, then $$\mathbb Q (z) : \mathbb Q = 2^n.$$ But the minimal…
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Solving Cubic Equations (With Origami)

I am working on a project about Mathematics and Origami. I am working on a section about how origami can be used to solve cubic equations. This is the source I am looking at: http://origami.ousaan.com/library/conste.html I understand the proof they…
user72195
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Solving Cubic Equations Using Origami

I have to write a research paper on a mathematical topic for my class; I chose the above topic. I understand that a parabola can be formed using a focus and directrix, both created by origami folds, and that Axiom 6 of Origami-Folding (Given two…
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The Mathematics of Coca Cola's Ribbon Wrapper.

I'm sorry if this is too vague a question or is otherwise deemed poor quality. The Background: I've just seen an advert for the (new?) Coca Cola festive ribbon wrapper. Here's a picture: A description of the ribbon making: One takes a tab on the…
Shaun
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Origami-constructible numbers

I apologize if this question has been asked here already; I am wondering whether it is known precisely what is the class of origami-constructible numbers? The class of compass-and-straightedge constructible numbers is the real quadratic closure of…
Anon
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Is there a mathematical way to fold a $20 dollar bill for compactness?

I had a strange thought. I used to carry a pill fob on my keys with an emergency $20 bill in it, before the whole thing got stolen. I always had some trouble fitting the bill inside the fob and barely managed it each time. I would fold it a couple…
Neil
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Regular pentagon from a square paper

I found this page with instructions to create a pentagon from a square paper: Fold the square in half to create a rectangle Mark half in the right side: Mark half in the down side: Fold from the lowest mark making the right mark be over the…
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Why do folded concentric circles and rectangles form a hyperbolic paraboloid?

Here is a "self-forming" origami that I made from folding concentric circles - it would also happen if I folded concentric rectangles. How can the fold shapes such a saddle-like geometry?
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Math and Origami

I am working on a project for class about the mathematics behind origami and write now I am looking into what is and is not constructible. I've gotten to the definition of origami constructible points which says the following: The set of origami…
user72195
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How does folding paper affect the geometry angles?

This is how you create equilateral triangles. But I have noticed that if you start of with a flawed fold, you can still end up with equilateral triangles, how come? Instructions: Need: Rectangular strip paper. Step one make an arbitrary…
MatJour
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Euclidean Geometry v.s. Origami Geometry

It's well known that you can't trisect an arbitrary angle with a traditional straight-edge and compass. However, using methods in traditional Origami, we can trisect an angle. Typically, when discussing these two topics, it's usually in light of…
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Simplest algorithm for edge coloring of a dodecahedron?

I have an origami model of a dodecahedron I am assembling. There are 30 edges with 3 colors of 10 each. I could use a diagram that gives a possible 3 color edge coloring. However, is there some sort of simple algorithm I can follow which will easily…
abnry
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How to conceptualize unintuitive topology?

I found Project Origami: Activities for Exploring Mathematics in my university's library the other day and quickly FUBAR'd (folded-up beyond all recognition) the couple sheets of paper I had with me at the time. I showed the book to a couple friends…
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Can origami math solve polynomial equations of degree greater than 3?

I heard that straight edge + compass can solve up to quadratic equations. I've also heard the Origami/Paper-folding can solve cubic equations. But can it solve higher-degree polynomial equations (e.g. quartic, quintic) in general? If not, is there a…
chausies
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Is there an exact solution for tan(36) using origami from a unit square?

This question is more for chagrins and curiosity than anything else: Is there a way to use origami to construct the tangent of 36 degrees (~0.7265425)? I've come up with the image below, which is accurate to about 5 decimal places (the exact…
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