Related papers: How they (should have) built the pyramids
The pyramid-to-dome transition in Ge$_{x}$Si$_{1-x}$ on Si(100) initiated by step bunching on pyramidal quantum dots is atomistically simulated using a novel multi-state lattice model incorporating effective surface reconstructions. Results…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
Wooden blocks are a common toy for infants, allowing them to develop motor skills and gain intuition about the physical behavior of the world. In this paper, we explore the ability of deep feed-forward models to learn such intuitive…
Slithering, crawling, slipping, gliding are various modes of limbless locomotion that have been mimicked for micro-manipulation of soft, slender and sessile objects. A lesser known mode is rolling which involves periodic, asymmetric and…
A reformulation of the three circles theorem of Johnson with distance coordinates to the vertices of a triangle is explicitly represented in a polynomial system and solved by symbolic computation. A similar polynomial system in distance…
In this paper, constructions of regular pentagon and decagon, and the calculation of the main trigonometric ratios of the corresponding central angles are approached. In this way, for didactic purposes, it is intended to show the reader…
We consider pyramids made of one-dimensional pieces of fixed integer length a and which may have pairwise overlaps of integer length from 1 to a. We prove that the number of pyramids of size m, i.e. consisting of m pieces, equals (am-1,m-1)…
Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process…
Granular materials are known to separate by size under a variety of circumstances. Experiments presented here and elucidated by modeling and MD simulation document a new segregation mechanism, namely segregation by friction. The experiments…
We investigate the folding problem that asks if a polygon P can be folded to a polyhedron Q for given P and Q. Recently, an efficient algorithm for this problem has been developed when Q is a box. We extend this idea to regular polyhedra,…
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces…
We investigate the migration of particles of different geometrical shapes and sizes in a scaled-up model of a gravity-driven deterministic lateral displacement (g-DLD) device. Specifically, particles move through a square array of…
We study the spontaneous folding of a 2D template of microscopic panels into a 3D pyramid, driven by thermal fluctuations. Combining numerical simulations and analytical calculations, we find that the total folding time is a non-monotonic…
A series of peculiar, visual alignments between the pyramids of the pharaohs of the 4, 5 and 6 Egyptian dynasties exists. These alignments governed from the very beginning the planning of the funerary monuments of successive kings and, in…
This research proposes a novel morphing structure with shells inspired by the movement of pillbugs. Instead of the pillbug body, a loopcoupled mechanism based on slider-crank mechanisms is utilized to achieve the rolling up and spreading…
Deployable polyhedrons can transform between Platonic and Archimedean polyhedrons to meet the demands of various engineering applications. However, the existing design solutions are often with multiple degrees of freedom and complicated…
In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbolic plane yields a $(h^2r)$-cube mosaic in space $\mathbf{H}^2\!\times\!\mathbf{R}$ and the definition of the pyramid is based on this…
We will discuss about a possible method of using the cubit rod by the architects and the surveyors of Ancient Egypt to measure and draw lengths, comparing it with the other interpretations present in Literature. Instead of the modern…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be not more, than three of them). We formulate conjectures and…