scholarly journals Origami folds in higher-dimension

10.29007/n76q ◽  
2018 ◽  
Author(s):  
Tetsuo Ida ◽  
Stephen Watt
Keyword(s):  
Euclidean Space ◽  
Half Plane ◽  
Higher Dimensions ◽  
Point Of View ◽  
Dimensional Euclidean Space ◽  
Higher Dimension ◽  
3 Dimensional ◽  
Axiomatic Treatment ◽  
The Subject

We present a generalization of mathematical origami to higher dimensions. We briefly explain Huzita- Justin’s axiomatic treatment of mathematical origami. Then, for concreteness, we apply it to origami on 3-dimensional Euclidean space in which the fold operation consists of selecting a half-plane and reflect- ing one half-plane across it. We finally revisit the subject from an n-dimensional point of view.

scholarly journals CURVES ON RULED SURFACES UNDER INFINITESIMAL BENDING

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Marija Najdanović ◽  
Miroslav Maksimović ◽  
Ljubica Velimirović
Keyword(s):  
Euclidean Space ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
Hyperbolic Paraboloid ◽  
3 Dimensional ◽  
Infinitesimal Bending

Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the bending of curves on the cylinder, the hyperbolic paraboloid and the helicoid are considered and appropriate bending fields are found. Some examples are graphically presented.

The Evaluation of Moments of Regions With Piecewise-Linearly Approximated Boundaries via Line Integration

1989 ◽  
Author(s):  
J. Angeles ◽  
M. J. Al-Daccak
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
Inertia Tensor ◽  
Divergence Theorem ◽  
Dimensional Euclidean Space ◽  
Repeated Application ◽  
The Subject ◽  
First Moment

Abstract The subject of this paper is the computation of the first three moments of bounded regions imbedded in the three-dimensional Euclidean space. The method adopted here is based upon a repeated application of Gauss’s Divergence Theorem to reduce the computation of the said moments — volume, vector first moment and inertia tensor — to line integration. Explicit, readily implementable formulae are developed to evaluate the said moments for arbitrary solids, given their piecewise-linearly approximated boundary. An example is included that illustrates the applicability of the formulae.

scholarly journals Constructing the relative neighborhood graph in 3-dimensional Euclidean space

1991 ◽  
Vol 31 (2) ◽  
pp. 181-191 ◽  
Author(s):  
Jerzy W. Jaromczyk ◽  
Mirosław Kowaluk
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Neighborhood Graph ◽  
3 Dimensional ◽  
Relative Neighborhood Graph

scholarly journals Spherical Embeddings of Symmetric Association Schemes in 3-Dimensional Euclidean Space

2019 ◽  
Vol 36 (2) ◽  
pp. 245-250 ◽  
Author(s):  
Eiichi Bannai ◽  
Da Zhao
Keyword(s):  
Euclidean Space ◽  
Association Schemes ◽  
Dimensional Euclidean Space ◽  
3 Dimensional

scholarly journals On Various Definitions of Capacity and Related Notions

1967 ◽  
Vol 30 ◽  
pp. 121-127 ◽  
Author(s):  
Makoto Ohtsuka
Keyword(s):  
Euclidean Space ◽  
Positive Charge ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
Electric Capacity ◽  
De La Vallée Poussin

The electric capacity of a conductor in the 3-dimensional euclidean space is defined as the ratio of a positive charge given to the conductor and the potential on its surface. The notion of capacity was defined mathematically first by N. Wiener [7] and developed by C. de la Vallée Poussin, O. Frostman and others. For the history we refer to Frostman’s thesis [2]. Recently studies were made on different definitions of capacity and related notions. We refer to M. Ohtsuka [4] and G. Choquet [1], for instance. In the present paper we shall investigate further some relations among various kinds of capacity and related notions. A part of the results was announced in a lecture of the author in 1962.

scholarly journals Surfaces of Finite III-type

2021 ◽  
Vol 15 ◽  
pp. 190-194
Author(s):  
Hassan Al-Zoubi
Keyword(s):  
Euclidean Space ◽  
Fundamental Form ◽  
Principal Curvature ◽  
Gauss Curvature ◽  
Dimensional Euclidean Space ◽  
Surfaces Of Revolution ◽  
3 Dimensional ◽  
The Third ◽  
Third Fundamental Form ◽  
Special Case

In this paper, we consider surfaces of revolution in the 3-dimensional Euclidean space E3 with nonvanishing Gauss curvature. We introduce the finite Chen type surfaces with respect to the third fundamental form of the surface. We present a special case of this family of surfaces of revolution in E3, namely, surfaces of revolution with R is constant, where R denotes the sum of the radii of the principal curvature of a surface.

scholarly journals On the second Gaussian curvature of ruled surfaces in Euclidean $3$-space

2006 ◽  
Vol 37 (3) ◽  
pp. 221-226 ◽  
Author(s):  
Dae Won Yoon
Keyword(s):  
Euclidean Space ◽  
Gaussian Curvature ◽  
Mean Curvature ◽  
Ruled Surface ◽  
Ruled Surfaces ◽  
Dimensional Euclidean Space ◽  
3 Dimensional ◽  
The Mean ◽  
Second Gaussian Curvature

In this paper, we mainly investigate non developable ruled surface in a 3-dimensional Euclidean space satisfying the equation $K_{II} = KH$ along each ruling, where $K$ is the Gaussian curvature, $H$ is the mean curvature and $K_{II}$ is the second Gaussian curvature.

Two Parametric Representations of a Circle in 3-Dimensional Euclidean Space

1964 ◽  
Vol 37 (2) ◽  
pp. 100
Author(s):  
Leo Unger
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
3 Dimensional
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