Results 211 to 220 of about 6,790 (254)

Equilateral, isosceles or obtuse? Getting the measure of the North Atlantic Triangle

, 2010
McCulloch, T.
core  

Torsion of Nonlocal Bars with Equilateral Triangle Cross Sections

Journal of Computational and Theoretical Nanoscience, 2013
The theory based on size dependent non-local elasticity theory can serve as a more reasonable and proper approach in mechanical modeling of micro and nano sized components of nano mechanical devices. In this work, a nonlocal bar with equilateral triangle
Mustafa Özgur Yaylı, Yaylı Mustafa Özgur   +1 more
exaly   +2 more sources

3-bar tensegrity units with non-equilateral triangle on an end plane [PDF]

Mechanics Research Communications, 2018
The well-known 3-bar prismatic tensegrity unit has equilateral triangles on the two end planes. In this paper, properties of the 3-bar tensegrity unit with non-equilateral triangle on one end plane are investigated.
Jingyao Zhang, Makoto Ohsaki
exaly   +2 more sources

The basic elliptic equations in an equilateral triangle [PDF]

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
In his deep and prolific investigations of heat diffusion, Lamé was led to the investigation of the eigenvalues and eigenfunctions of the Laplace operator in an equilateral triangle. In particular, he derived explicit results for the Dirichlet and Neumann cases using an ingenious change of variables.
A S Fokas
exaly   +3 more sources

Packing a triangle by equilateral triangles of harmonic sidelengths

Discrete Mathematics
We say that planar convex bodies \(C_1, C_2, \dots\) can be packed into a planar convex body \(C\) if it is possible to apply translations and rotations to the bodies \(C_n\) so that the resulting translated and rotated bodies are contained in \(C\) and have mutually disjoint interiors.
Janusz Januszewski, Łukasz Zielonka
exaly   +3 more sources

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On Partitions of an Equilateral Triangle

Canadian Journal of Mathematics, 1967
Let T denote a closed unit equilateral triangle. For a fixed integer n, let dn denote the infimum of all those x for which it is possible to partition T into n subsets, each subset having a diameter not exceeding x. We recall that the diameter of a plane set A is given bywhere ρ (a, b) is the Euclidean distance between a and b.In this note we ...
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The Eigenvalues of an Equilateral Triangle

SIAM Journal on Mathematical Analysis, 1980
Let D be an equilateral triangle of side 1. We consider solutions of $\Delta u + \lambda u = 0$ in D with either the boundary condition $u = 0$ or ${{\partial u} / {\partial n }} = 0$. Let $n(\lambda )$ be the number of distinct eigenvalues $ \leqq \lambda $, $N(\lambda )$ be the total number of eigenvalues $ \leqq \lambda $, including multiplicities ...
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The dissection of equilateral triangles into equilateral triangles

Mathematical Proceedings of the Cambridge Philosophical Society, 1948
In a previous joint paper (‘The dissection of rectangles into squares’, by R. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte, Duke Math. J. 7 (1940), 312–40), hereafter referred to as (A) for brevity, it was shown that it is possible to dissect a square into smaller unequal squares in an infinite number of ways.
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Completeness of the Eigenfunctions of the Equilateral Triangle

SIAM Journal on Mathematical Analysis, 1985
The Dirichlet problem for the operator -\(\Delta\) in the equilaternal triangle is considered. Explicit expressions for its eigenvalues and eigenfunctions are given in terms of orbits of a certain group G. This group G has six elements and is defined as a set of transformations of \({\mathbb{Z}}^ 2\) generated by operations \(S_ 1: (m,n)\to (m,m-n ...
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