scholarly journals ISOSCELES TRIANGLES ON THE SIDES OF A TRIANGLE

2019 ◽  
Vol 9 (1) ◽  
pp. 123-130
Author(s):  
Sead Rešić ◽  
◽  
Alma Šehanović ◽  
Amila Osmić ◽  
◽  
...  
Keyword(s):  
Equilateral Triangles ◽  
Isosceles Triangles

Famous construction of Fermat-Toricelly point of a triangle leads to the question is there a similar way to construct other isogonic centers of a triangle in a similar way. For a purpose we remember that Fermat-Torricelli point of a triangle ΔABC is obtained by constructing equilateral triangles outwardly on the sides AB,BC and CA. If we denote thirth vertices of those triangles by C1 ,A1 and B1 respectively, then the lines AA1 ,BB1 and CC1 concurr at the Fermat-Torricelli point of a triangle ΔABC (Van Lamoen, 2003). In this work we present the condition for the concurrence, of the lines AA1 ,BB1 and C1 , where C1 ,A1 and B1 are the vertices of an isosceles triangles constructed on the sides AB,BC and CA (not necessarily outwordly) of a triangle ΔABC. The angles at this work are strictly positive directed so we recommend the reader to pay attention to this fact.

Buckling of Isosceles Triangular Plates

1969 ◽  
Vol 73 (703) ◽  
pp. 604
Author(s):  
J. Lockwood Taylor
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Infinite Series ◽  
Series Solution ◽  
Technical Note ◽  
Buckling Load ◽  
Data Sheet ◽  
Trigonometrical Series ◽  
Equilateral Triangles ◽  
Isosceles Triangles

Application of a method suggested by my technical note on equilateral and semi-equilateral triangles has yielded values for the buckling coefficients for isosceles triangles which in some cases differ appreciably from those given on Data Sheet 02.04.06. The technical note quoted gives exact solutions in the form of a terminating trigonometrical series. When the triangle becomes isosceles, the series no longer terminates, but the infinite series solution, on insertion of the boundary conditions, gives an infinite determinant for the buckling load or eigenvalue. Evaluation of the determinant, or of a sufficient number of terms, was computed on a Univac 1107, with the following results, which have been converted to the notation of Data Sheet 02.04.06.

The crystal structure of BiTel

1993 ◽  
Vol 204 (1) ◽  
Author(s):  
K. G. Keramidas ◽  
G. P. Voutsas ◽  
A. Papazoglou ◽  
P. I. Rentzeperis
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Least Squares ◽  
Three Dimensional ◽  
Full Matrix ◽  
Anisotropic Temperature ◽  
Equilateral Triangles ◽  
Computer Controlled ◽  
Temperature Factors ◽  
Isosceles Triangles

AbstractThe crystal structure of BiTeI has been redetermined with 1924 independent reflections, using three-dimensional intensities measured on a computer controlled Philips PW 1100 single crystal diffractometer. The structure belongs to the rhombohedral space groupThe positional and thermal parameters, with anisotropic temperature factors, were refined by full-matrix least-squares calculations to a finalEach Bi atom is six-coordinated by three Te and three I atoms at distances 3.88(5) Å and 3.05(2) Å respectively thus forming a distorted octahedron. The faces of the octahedron are two equilateral triangles (Te-Te-Te, I-I-I) with sides 4.336 Å and six isosceles triangles (three I-Te-I and three Te-I-Te) with sides I–Te 3.29(3) Å and I–I or Te–Te 4.336 Å.The octahedra are linked to each other by a common Te–I edge along the

scholarly journals Optimal Local Routing on Delaunay Triangulations Defined by Empty Equilateral Triangles

2015 ◽  
Vol 44 (6) ◽  
pp. 1626-1649 ◽  
Author(s):  
Prosenjit Bose ◽  
Rolf Fagerberg ◽  
André van Renssen ◽  
Sander Verdonschot
Keyword(s):  
Delaunay Triangulations ◽  
Equilateral Triangles ◽  
Local Routing

scholarly journals BioFilm©

2000 ◽  
Vol 8 (2) ◽  
pp. 6-7
Author(s):  
Lee van Hook
Keyword(s):  
Recent Article ◽  
Metal Halide ◽  
Toxic Effects ◽  
Polymer Science ◽  
Complex Combination ◽  
Dry Biomass ◽  
Equilateral Triangles ◽  
Silver Grains

Photographic chemistry has long been a complex combination of inorganic metal-halide and organic chemistries and polymer science. We at the P.R.I, have managed to add biology to this stew.Silver has long been known as a toxicelement to microbes, and so used as a drug to kill bacteria. But there are bacteria that can survive in environments high in silver. It has been reported that some bacteria can accumulate up to 25% of their dry biomass as silver, and so acquire resistance to the toxic effects of silver. Also, a recent article in the Proc. Nat. Acad.Sci. describes the intracellular deposition of silver grains in such shapes as hexagons and equilateral triangles.

A fast and robust circle detection method using isosceles triangles sampling

2016 ◽  
Vol 54 ◽  
pp. 218-228 ◽  
Author(s):  
Hanqing Zhang ◽  
Krister Wiklund ◽  
Magnus Andersson
Keyword(s):  
Detection Method ◽  
Circle Detection ◽  
Isosceles Triangles

Central configurations of the five-body problem with two isosceles triangles

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia ◽  
Luis Fernando Mello ◽  
Lucas Ruiz dos Santos
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Isosceles Triangles

Vibration of Triangular Cantilever Plates by the Ritz Method

1954 ◽  
Vol 21 (4) ◽  
pp. 365-370
Author(s):  
B. W. Andersen
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Plan View ◽  
Modes Of Vibration ◽  
Accuracy Of Results ◽  
Isosceles Triangles

Abstract Using the method published by Ritz in 1909, natural frequencies and corresponding node lines have been determined for two symmetric and two antisymmetric modes of vibration of isosceles triangular plates clamped at the base and having length-to-base ratios of 1, 2, 4, and 7 and for the two lowest modes of right triangular plates clamped along one leg and having ratios of the length of the free leg to that of the clamped one of 2, 4, and 7. A nonorthogonal co-ordinate system was used which gave constant limits of integration over the area of the triangle. The co-ordinate transformation made it necessary to modify the functions used by Ritz in approximating deflections and to consider cross products in the integration. The integration was done numerically, using tables compiled by Young and Felgar in 1949. To check the accuracy of results, a solution was obtained to the problem of a vibrating cantilever beam of uniform depth and triangular plan view. The results obtained were found to be consistent with those obtained for the plates by using an eight-term series to approximate the deflections of the symmetric plates (isosceles triangles) and a six-term series to approximate the deflections of the unsymmetric plates (right triangles).

scholarly journals Sustainable Geometric and Bio-Cultural/Cultural Models of Human Society: The Role of Non-Capitalist Cooperation in Times of Civilizational/Environmental Crisis

2017 ◽  
Vol 10 (2) ◽  
pp. 13
Author(s):  
M. S. Sthel ◽  
J. G. R. Tostes ◽  
J. R. Tavares
Keyword(s):  
Carbon Footprint ◽  
Cultural Models ◽  
Total Carbon ◽  
Environmental Crisis ◽  
Human Society ◽  
Capitalist System ◽  
Equilateral Triangles ◽  
Footprint Area ◽  
The Individual

The Sustainable Complex Triangular Cells (SCTC) and bio-cultural/cultural models of human society are employed here. Regarding SCTC model, the cell areas represent the individual´s carbon footprint. Scalene triangles represent each individual in the present competitive standard (inward arrows). Equilateral triangles (outward arrows) are “summed” so as forming cooperative-hexagonal bodies leading to a collaborative model of society, reducing the total carbon footprint area as regard the formal analogous sum of each individual (inward) non-cooperative triangle. We particularly have focused on environmental global limits of the capitalist system, with SCTC modeling an accelerated global anti-ecological “scalenization” process from the 29 crisis to the present neoliberal stage of capitalism. Employing again the SCTC model, we describe and exemplify instable and short lifetime “islands” built up through evanescent local process of “cooperative equilateralization” (outward arrows) in the last 40 years. Such non-capitalist features were “mixed in” with competitive “scalenized” features of the capitalist “ocean”. In the final topic, we will consider bio-cultural (Nowak and Wilson) models of the human history and a cultural (Weber-Alberoni) model for great inflexions in the western history. All these models intersect via human cooperation. Particularly, that last model is complementary to the above small and instable “islands” sketch: but now we deal with western religious and secular, non- capitalist, purely cooperative experiences, which correspond to the above labeled SCTC “cooperative equilateralization”. Such weber-alberonian “islands” may be – some few times - sufficiently stable for rapid and great expansions leading, e.g., to a “civilizational/environmental jump” in the presently menaced planet.

scholarly journals Discrete Dimers of Redox-Active and Fluorescent Perylene Diimide-Based Rigid Isosceles Triangles in the Solid State

2018 ◽  
Vol 141 (3) ◽  
pp. 1290-1303 ◽  
Author(s):  
Siva Krishna Mohan Nalluri ◽  
Jiawang Zhou ◽  
Tao Cheng ◽  
Zhichang Liu ◽  
Minh T. Nguyen ◽  
...  
Keyword(s):  
Solid State ◽  
Perylene Diimide ◽  
Redox Active ◽  
Isosceles Triangles
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