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...

cut. The solution, known as the fold-and-cut theorem, states that any shape with straight sides can be obtained. A practical problem is how to fold a...

fold the paper flat, or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane (see fold-and-cut...

given polygon can be cut from it with a single straight cut (the fold-and-cut theorem), and related origami design problems. Barequet et al. use straight...

she published the first proof of the fold-and-cut theorem in mathematical origami. In graph drawing, Hutton and Lubiw found a polynomial time algorithm...

mandatory folding. An online version of the craft is known as "Make-A-Flake", and was created by Barkley Inc. in 2008. Fold-and-cut theorem Kirigami Boeckmann...

theorem in its basic form was based on the observation that the rotational symmetries of a crystal are usually limited to 2-fold, 3-fold, 4-fold, and...

Lang using tree structures and circle packing to automate the design of origami folding patterns, the fold-and-cut theorem according to which any polygon...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

from the cut locus and p {\displaystyle p} . This idea is used in the local Laplacian comparison theorem and the local Hessian comparison theorem. These...

The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between...

Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are...

constructed from existing lines and points. When folding rigid origami flat, Kawasaki's theorem and Maekawa's theorem restrict the folding patterns that are possible...

This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures...

one can first "accordion fold" the strip in its wide direction back and forth using an even number of folds. With two folds, for example, a 1 × 1 {\displaystyle...

which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry...

An extension of Mantel's Theorem provides an explicit lower bound on triangle densities in terms of edge densities. Theorem (Goodman). t ( K 3 , G ) ≥...

curvature/flat, and negative curvature/hyperbolic – and the geometrization conjecture (now theorem) in 3 dimensions – every 3-manifold can be cut into pieces...

The theorem is named for Anders Johan Lexell, who presented a paper about it c. 1777 (published 1784) including both a trigonometric proof and a geometric...

setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, we randomly shuffle the dataset into two sets d0 and d1, so that both sets are...

way (e.g., from an apparently unrelated theorem or a collection of theorems). A proof that is based on new and original insights. A method of proof that...

transformation to change z = −1 to z = 1 and then using Gauss's theorem to evaluate the result. A typical example is Kummer's theorem, named for Ernst Kummer: 2 F...

n-holed tori (or, rarely, n-fold tori). The terms double torus and triple torus are also occasionally used. The classification theorem for surfaces states that...

be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge...

symmetries of field extensions, provides an elegant proof of the Abel-Ruffini theorem that general quintic equations cannot be solved in radicals. Fields serve...

Property of Equiangular Polygons: What Is It About? a discussion of Viviani's theorem at Cut-the-knot. Weisstein, Eric W. "Equiangular Polygon". MathWorld....

MR 3195329. Leighton, Tom; Rao, Satish (1999). "Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms". Journal of the ACM...

known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions...

to the classical crystallographic restriction theorem, can possess only two-, three-, four-, and six-fold rotational symmetries, the Bragg diffraction...

proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi ( π {\displaystyle \pi } ) is a transcendental number...