Results 1 to 10 of about 36,861 (169)
Equilateral triangle and the Holy Trinity
Journal of Architecture and Urbanism, 2014 The paper deals with architectural space designed and/or built on an equilateral triangular plan, and designated for a sacred function. The author discusses the exceptional features of equilateral triangle in comparison to other central layouts.
J. Krzysztof Lenartowicz
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An Interactive Control Algorithm Used for Equilateral Triangle Formation with Robotic Sensors [PDF]
Sensors, 2014 This paper describes an interactive control algorithm, called Triangle Formation Algorithm (TFA), used for three neighboring robotic sensors which are distributed randomly to self-organize into and equilateral triangle (E) formation.
Xiang Li, Hongcai Chen
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Apollonian Equilateral Triangles [PDF]
, 2013 Given an equilateral triangle with $a$ the square of its side length and a point in its plane with $b$, $c$, $d$ the squares of the distances from the point to the vertices of the triangle, it can be computed that $a$, $b$, $c$, $d$ satisfy $3(a^2+b^2+c^2+d^2)=(a+b+c+d)^2$. This paper derives properties of quadruples of nonnegative integers $(a,\, b,\,
Chen, Christina, Li, Nan
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Courant-Sharp Eigenvalues for the Equilateral Torus, and for the Equilateral Triangle [PDF]
Letters in Mathematical Physics, 2016 Slight modifications and some misprints ...
Bérard, Pierre, Helffer, Bernard
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Quantization for uniform distributions on equilateral triangles [PDF]
, 2015 We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical optimization results for $n\leq 21$, and a bound on the quantization error for $n\to\infty$.
Dettmann, Carl, Roychowdhury, Mrinal
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Tiling an Equilateral Triangle
, 2018 Let $ABC$ be an equilateral triangle. For certain triangles $T$ (the "tile") and certain $N$, it is possible to cut $ABC$ into $N$ copies of $T$. It is known that only certain shapes of $T$ are possible, but until now very little was known about the possible values of $N$. Here we prove that for $N>3$, $N$ cannot be prime, and study more closely the
Beeson, Michael
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AIP Advances, 2023 In this paper, we studied the effect of the 2D epoxy thin films’ shape with equilateral triangle and square structures, and matrix size Lx × Ly of (10 × 9), (20 × 19), (30 × 29), and (40 × 39) with equilateral triangle structure and (10 × 10), (20 × 20),
Dung Nguyen Trong +2 more
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Packing and Covering a Unit Equilateral Triangle with Equilateral Triangles [PDF]
The Electronic Journal of Combinatorics, 2005 Packing and covering are elementary but very important in combinatorial geometry, they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle with smaller triangles which is originated from one of Erdős' favorite problems.
Zhang, Yuqin, Fan, Yonghui
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Numerical study of the passive micromixer with the novel blocks
AIP Advances, 2022 The micromixer is a key component of the microfluidic chip analysis system. Micromixers are widely used in applications, such as DNA hybridization and protein synthesis. A high-efficiency mixer can speed up the biochemical analysis process.
Zhongli Wu +5 more
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Emergent geometry and duality in the carbon nucleus
Nature Communications, 2023 The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, 12C, is similarly full of multifaceted complexity.
Shihang Shen +5 more
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