Results 11 to 20 of about 6,790 (254)
On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle [PDF]
AxiomsThe possible positions of an equilateral triangle whose vertices are located on the support sides of a generic triangle are studied. Using complex coordinates, we show that there are infinitely many such configurations, then we prove that the centroids ...
Dorin Andrica, Ovidiu Bagdasar
exaly +4 more sources
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
doaj +2 more sources
An enumeration of equilateral triangle dissections
Discrete Applied Mathematics, 2010 We enumerate all dissections of an equilateral triangle into smaller equilateral triangles up to size 20, where each triangle has integer side lengths. A perfect dissection has no two triangles of the same side, counting up- and down-oriented triangles ...
Hämäläinen, Carlo, Drápal, Aleš
core +4 more sources
Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle [PDF]
Letters in Mathematical Physics, 2016 International audienceWe address the question of determining the eigenvalues $\lambda_n$ (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with $
Bérard, Pierre, Helffer, Bernard
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, 2020 In any triangle, the perpendicular side bisectors meet the corresponding internal angle bisectors on the circumcircle. If we take those three points as the vertices of a new triangle and repeat the operation indefinitly, we end up in the limit with a par
Buysse, Martin
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Eigenstructure of the equilateral triangle. Part III. The Robin problem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 Lamé's formulas for the eigenvalues and eigenfunctions of the Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the Robin boundary condition.
Brian J. McCartin
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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 ...
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.
Yuqin Zhang, Yonghui Fan
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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
doaj +1 more source