Related papers: Exploring criteria for designing novel waterbomb t…
We consider tessellations of the Euclidean $(d-1)$-sphere by $(d-2)$-dimensional great subspheres or, equivalently, tessellations of Euclidean $d$-space by hyperplanes through the origin; these we call conical tessellations. For random…
In the previous manuscript, new tilings (tessellations) were presented using convex pentagonal tiles belonging to Type 1 and Type 5. The convex pentagon tilings are related to heptiamond tilings. Later, the authors found Johannes Hindriks'…
M.C. Eschers tessellations have captured the imaginations of both artists and mathematicians. Circle Limit III is the most intricate of his tessellations, featuring patterns that repeat at increasingly fine scales. Although his patterns…
Two mathematical aspects of the centuries-old Japanese sashiko stitching form hitomezashi are discussed: the encoding of designs using words from a binary alphabet, and duality. Traditional hitomezashi designs are analysed using these two…
This paper proposes a family of origami tessellations called extruded Miura-Ori, whose folded state lies between two parallel planes with some faces on the planes, potentially useful for folded core materials because of face bonding. An…
Over the past decade, we have designed six typefaces based on mathematical theorems and open problems, specifically computational geometry. These typefaces expose the general public in a unique way to intriguing results and hard problems in…
Adopting the global approach to tangent bundles of order two established in[1], we develop this approach to find new results. We also generalize various results of [3], [4] and [6] to the geometry of tangent bundles of order two.
A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting…
The rheology of molecular brushes remains challenging to control due to the multiple length scales and relaxation processes involved and the lack of direct observation of molecular conformation during flow. We use molecular dynamics…
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…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…
We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original…
Bistable mechanical systems exhibit two stable configurations where the elastic energy is locally minimized. To realize such systems, origami techniques have been proposed as a versatile platform to design deployable structures with both…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Programmable folding of elastic sheets typically relies on predefined flexible creases or active materials-enabled hinges, which lack intrinsic bistability and limit reprogrammability within a single structure. Here, we present a…
We study projective schemes arising from eigenvectors of tensors, called eigenschemes. After some general results, we give a birational description of the variety parametrizing eigenschemes of general ternary symmetric tensors and we…
Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, we exploit kirigami…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
We discuss here the geometry of frieze patterns, and add a few words about Greek vases, molecular symmetry, and 2D crystallography. The work is written primarily for school students.