The Helium Stockpile: A Collaboration in Mathematical Folding Sculpture

Leonardo ◽  
2006 ◽  
Vol 39 (3) ◽  
pp. 233-235 ◽  
Author(s):  
Eric D. Demaine ◽  
Martin L. Demaine ◽  
A. Laurie Palmer
Keyword(s):  
Three Dimensional ◽  
Dimensional Chain ◽  
Mathematical Basis ◽  
One Dimensional ◽  
Dimensional Shape ◽  
Folding Structure ◽  
Three Dimensional Shape

The Helium Stockpile is a manipulable folding structure of hundreds of wooden blocks, representing the transformation between surface and solid through a foldable one-dimensional chain. The sculpture grew out of an unexpected collaboration between a sculptor and two mathematicians, giving the structure a mathematical basis through which it is guaranteed to be foldable into essentially any three-dimensional shape.

New Spectral Decomposition Method for Three-Dimensional Shape Models and Its Applications

2005 ◽  
Vol 5 (4) ◽  
pp. 277-282 ◽  
Author(s):  
Kohei Murotani ◽  
Kokichi Sugihara
Keyword(s):  
Singular Spectrum Analysis ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
One Dimensional ◽  
Autocorrelation Matrix ◽  
Shape Models ◽  
Analysis Technique ◽  
Dimensional Shape ◽  
Mutual Relations ◽  
Three Dimensional Shape

This paper presents a generalization of a data analysis technique called a singular spectrum analysis (SSA). The original SSA is a tool for analyzing one-dimensional data such as time series, whereas the generalization presented in this paper is suitable for multidimensional data such as three-dimensional polygonal meshes. The basic idea is to generalize the autocorrelation matrix so as to represent mutual relations of multidimensional data flexibly. Two applications of the proposed generalization are also shown briefly.

scholarly journals Can a flux-based mechanism explain positioning of protein clusters in a three-dimensional cell geometry?

2018 ◽  
Author(s):  
Matthias Kober ◽  
Silke Bergeler ◽  
Erwin Frey
Keyword(s):  
Cell Division ◽  
Three Dimensional ◽  
Stochastic Simulations ◽  
Bacterial Cell Division ◽  
Cell Geometry ◽  
One Dimensional ◽  
Protein Clusters ◽  
Dimensional Shape ◽  
Three Dimensional Shape ◽  
Dimensional Cell

The plane of bacterial cell division must be precisely positioned. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a large cluster, which is tethered to the nucleoid by the ATPase PomZ and moves in a stochastic, but biased manner towards midcell, where it initiates cell division. Previously, a positioning mechanism based on the fluxes of PomZ on the nucleoid was proposed. However, the cluster dynamics was analyzed in a reduced, one-dimensional geometry. Here we introduce a mathematical model that accounts for the three-dimensional shape of the nucleoid, such that nucleoid-bound PomZ dimers can diffuse past the cluster without interacting with it. Using stochastic simulations, we find that the cluster still moves to and localizes at midcell. Redistribution of PomZ by diffusion in the cytosol is essential for this cluster dynamics. Our mechanism also positions two clusters equidistantly on the nucleoid. We conclude that a flux-based mechanism allows for cluster positioning in a biologically realistic three-dimensional cell geometry.

Four Dimensions of Diamond T: Combination Trade Marks of Colours And Shapes

2006 ◽  
Vol 37 (4) ◽  
pp. 583
Author(s):  
Michael McGowan
Keyword(s):  
Three Dimensional ◽  
Trade Mark ◽  
Fourth Dimension ◽  
Trade Marks ◽  
Four Dimensions ◽  
Trade Mark Law ◽  
Dimensional Shape ◽  
Three Dimensional Shape

This article examines the relatively new fields of colour and shape trade marks. It was initially feared by some academics that the new marks would encroach on the realms of patent and copyright.  However, the traditional requirements of trade mark law, such as functionality and descriptiveness, have meant that trade marks in colour and shape are extremely hard to acquire if they do not have factual distinctiveness. As colour and shape trade marks have no special restrictions, it is proposed that the combination trade mark theory and analysis from the Diamond T case should be used as a way to make them more accessible. The combination analysis can be easily applied because every product has a three dimensional shape and a fourth dimension of colour.

Acoustic Analysis of Detailed Three-Dimensional Shape of the Human Nasal Cavity and Paranasal Sinuses

2017 ◽  
Author(s):  
Tatsuya Kitamura ◽  
Hironori Takemoto ◽  
Hisanori Makinae ◽  
Tetsutaro Yamaguchi ◽  
Kotaro Maki
Keyword(s):  
Nasal Cavity ◽  
Paranasal Sinuses ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Dimensional Shape ◽  
Three Dimensional Shape
Sign in / Sign up

Export Citation Format

Share Document