相关论文: Origami constructions
A realisation of a graph in the plane as a bar-joint framework is rigid if there are finitely many other realisations, up to isometries, with the same edge lengths. Each of these finitely-many realisations can be seen as a solution to a…
For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworking techniques. Further, this paper provides an analysis of…
There are only a few invariants one classically associates with precompact translation surfaces, among them certain numberfields, i.e. fields which are finite extensions of the field Q of rational numbers. These fields are closely related…
We describe the construction of the slice fibration of a given one.
Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled…
In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian…
The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics, and mechanical metamaterials. However, finding foldable paths can be a formidable task as the…
Rigid foldability allows an origami pattern to fold about crease lines without twisting or stretching component panels. It enables folding of rigid materials, facilitating the design of foldable structures. Recent study shows that rigid…
Large sets of equiangular lines are constructed from sets of mutually unbiased bases, over both the complex and the real numbers.
We survey results on the foldability of flat origami models. The main topics are the question of when a given crease pattern can fold flat, the combinatorics of mountain and valley creases, and counting how many ways a given crease pattern…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as…
Define the augmented square twist origami crease pattern to be the classic square twist crease pattern with one crease added along a diagonal of the twisted square. In this paper we fully describe the rigid foldability of this new crease…
We prove astonishing identities generated by compositions of positive integers. In passing, we obtain two new identities for Stirling numbers of the first kind. In the two last sections we clarify an algebraic sense of these identities and…
This is my dissertation about digraphs ordered by pp-constructability. We study in particular smooth digraphs, i.e., digraphs without sources or sinks, tournaments and semicomplete digraphs, orientations of paths and cycles, digraphs with…
We report on a recent implementation of patchworking and real tropical hypersurfaces in $\texttt{polymake}$. As a new mathematical contribution we provide a census of Betti numbers of real tropical surfaces.
An efficient way to introduce elastic energy that can bias an origami structure toward desired shapes is to allow curved tiles between the creases. The bending of the tiles supplies the energy and the tiles themselves may have additional…
See hep-th/9903228.
Many of the patterns seen in Origami are currently being explored as a platform for building functional engineering systems with versatile characteristics that cater to niche applications in various technological fields. One such pattern is…
We provide a variant of an axiomatization of elementary geometry based on logical axioms in the spirit of Huzita--Justin axioms for the Origami constructions. We isolate the fragments corresponding to natural classes of Origami…