相关论文: Origami constructions
In this paper, we construct certain infinite families of imaginary quadratic fields whose class number is divisible by a given positive integer.
We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zero-thickness paper. In contrast, we show that the…
For any positive integer $r$, we construct a smooth complex projective rational surface which has at least $r$ real forms not isomorphic over $\mathbb{R}$.
Simple closed curves in the plane can be mapped to nontrivial knots under the action of origami foldings that allow the paper to self-intersect. We show all tame knot types may be produced in this manner, motivating the development of a new…
An "origami" (or flat structure) on a closed oriented surface, $S_g$, of genus $g \geq 2$ is obtained from a finite collection of unit Euclidean squares by gluing each right edge to a left one and each top edge to a bottom one. The main…
Rigid origami has shown potential in large diversity of practical applications. However, current rigid origami crease pattern design mostly relies on known tessellations. This strongly limits the diversity and novelty of patterns that can…
We construct rings of typed ordered fuzzy numbers whose component functions are of a common form. As this ring also contains improper fuzzy numbers (OFNs whose membership "functions" are actually just relations), we develop a set of…
We are introducing a general framework for the construction of polyhedra and simplicial comlexes that are {\em bifoldable}, i.e. foldable into two two different planes. This vastly generalizes Origami folds known as the Miura pattern, the…
A conjecture regarding the structure of expander graphs is discussed.
We give explicit origami embeddings of a 2-dimensional flat torus of any modulus in the 3-dimensional Euclidean space.
This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.
Origami has shown the potential to approximate three-dimensional curved surfaces by folding through designed crease patterns on flat materials. The Miura-ori tessellation is a widely used pattern in engineering and tiles the plane when…
Origami, the traditional paper-folding art, has inspired the modern design of numerous flexible structures in science and engineering. In particular, origami structures with different physical properties have been studied and utilized for…
It has been known since 1996 that deciding whether a collection of creases on a piece of paper can be fully folded flat without causing self-intersection or adding new creases is an NP-Hard problem (Bern and Hayes). In their proof, a binary…
In this expository article, the real numbers are defined as infinite decimals. After defining an ordering relation and the arithmetic operations, it is shown that the set of real numbers is a complete ordered field. It is further shown that…
This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and…
Twisting sheets as a strategy to form functional yarns relies on millennia of human practice in making catguts and fabric wearables, but still lacks overarching principles to guide their intricate architectures. We show that twisted…
A family of algebraic surfaces with many nondegenerate real singularities is introduced with the help of a construction, which has been used in previous works for the generation of substitution tilings.
This is an example on the cohomology of threefolds.
We give a constructive proof using tropical modifications of the existence of a family of real algebraic plane curves with asymptotically maximal numbers of even ovals.