Related papers: Higher dimensional origami constructions
Origami and Kirigami, the famous Japanese art forms of paper folding and cutting, have inspired the design of novel materials & structures utilizing their geometry. In this article, we explore the geometry of the lesser known popup art,…
This article explores the limits of geometric construction using various tools, both classical and modern. Starting with ruler and compass constructions, we examine how adding methods such as origami, marked rulers (neusis), conic sections,…
This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…
In this paper, we will show methods to interpret some rigid origami with higher degree vertices as the limit case of structures with degree-4 supplementary angle vertices. The interpretation is based on separating each crease into two…
This paper gives one set of axioms for origami constructions, and describes the set of constructible points under these axioms. The determination of the set of cunstructible points for this particular set of axioms is related to Hilbert's…
We discuss well known geometric constructions via paper-folding. The note is written primary for school students.
One-dimensional slender bodies can be deformed or shaped into spatially complex curves relatively easily due to their inherent compliance. However, traditional methods of fabricating complex spatial shapes are cumbersome, prone to error…
Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms…
Kirigami, art of paper cutting, enables two-dimensional sheets transforming into unique shapes which are also hard to reshape once with prescribed cutting patterns. Rare kirigami designs manipulate cuts on three-dimensional objects to…
The ancient art of origami, traditionally used to transform simple sheets into intricate objects, also holds potential for diverse engineering applications, such as shape morphing and robotics. In this study, we demonstrate that one of the…
Here we describe an ultra-low-cost origami-based approach for large-scale manufacturing of microscopes, specifically demonstrating brightfield, darkfield, and fluorescence microscopes. Merging principles of optical design with origami…
For centuries, human civilizations devised metal forming techniques to make tools and items; yet, customized metal forming remains costly and intricate. Laser-forming origami} (lasergami) is a metal forming process where a laser beam cuts…
We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First,…
This paper shows a cut along a crease on an origami sheet makes simple modeling of popular traditional basic folds such as a squash fold in computational origami. The cut operation can be applied to other classical folds and significantly…
We investigate the graphs formed from the vertices and creases of an origami pattern that can be folded flat along all of its creases. As we show, this is possible for a tree if and only if the internal vertices of the tree all have even…
The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…
We present a formalization of geometric instruments that considers separately geometric and arithmetic aspects of them. We introduce the concept of tool, which formalizes a physical instrument as a set of axioms representing its geometric…
Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, non-trivial geometry can be created through…
An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a…
This article reviews the so-called "axioms" of origami (paper folding), which are elementary single-fold operations to achieve incidences between points and lines in a sheet of paper. The geometry of reflections is applied, and exhaustive…