Questions tagged [origami-folding]

For mathematical questions related to origami and other aspects of folding.

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Solution for the sequence of the number of “major flaps” in origami bases and its relation to other sequences

I have recently been getting into origami and reading Robert J. Lang's (a physicist and one of the leading modern origami artist) books. In the book Origami Design Secrets he showed a sequence of more ...
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1answer
42 views

Folding a non-rectangular shape into a rectangle of uniform thickness

I think the following might be an interesting subproblem of this question: Question: For an odd number $n\ge 3$, is there a non-rectangular but still convex shape of area $A=1$, that can be folded (...
6
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1answer
347 views

Napkin Folding Problem / Rumpled Ruble Problem

I am an outsider to this group. I'm a journalist and am working on a piece about theoretical math/geometry. Simply put, when a napkin is folder in such a way to increase its perimeter is that strictly ...
49
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3answers
4k views

Is the “Napkin conjecture” open? (origami)

The falsity of the following conjecture would be a nice counter-intuitive fact. Given a square sheet of perimeter $P$, when folding it along origami moves, you end up with some polygonal flat figure ...
16
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1answer
1k views

Origami Constructions: Intersecting two Circles

It is well known that every construction that can be performed with compass and straightedge alone can also be performed using origami, see: R. Geretschlager. Euclidean Constructions and the Geometry ...
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2answers
1k views

Four Dimensional Origami Axioms

What are the axioms of four dimensional Origami. If standard Origami is considered three dimensional, it has points, lines, surfaces and folds to create a three dimensional form from the folded ...