Filters

18,046 Hits in 7.3 sec

### On the Maximum Number of Equilateral Triangles, I

B. M. Ábrego, S. Fernández-Merchant
2000 Discrete & Computational Geometry
The following problem was posed by Erdős and Purdy: "What is the maximum number of equilateral triangles determined by a set of n points in R d ?"  ...  In addition it is shown that for d = 2 the maximum is attained by subsets of the regular triangle lattice.  ...  In this article we address one of them. "What is the maximum number of equilateral triangles that can be determined by n points in the plane?"  ...

### Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics

Wen Luo, Jinbo Liu, Zengrui Li, Jiming Song
2020 IEEE Open Journal of Antennas and Propagation
The interpolation errors of the higher order bivariate Lagrange polynomial interpolation based on the rectangular, right and equilateral triangular interpolations are measured by using the maximum and  ...  On the other hand, the equilateral triangular interpolation using the regions inside a big triangle as interpolation area is proved to be the most accurate interpolation method.  ...  For the same maximum error, the equilateral triangular interpolation needs the same number of samples per wavelength as the rectangular interpolation, which is less than that of the right triangular one  ...

### Efficient Triangular Interpolation Method: Error Analysis and Applications

Wen Luo, Jinbo Liu, Zengrui Li, Jiming Song
2020 IEEE Antennas and Wireless Propagation Letters
The maximum and root-mean-square (RMS) errors on the right triangular, equilateral triangular and rectangular (bivariate Lagrange polynomial) interpolations are analyzed.  ...  It is found that the maximum and RMS errors are directly proportional to the (p+1)'th power of kh for both one-dimensional (1D) and two-dimensional (2D, bivariate) interpolations, where k is the wavenumber  ...  The maximum errors of the equilateral triangular interpolation are the same as the rectangular one, while the former one has the lowest RMS errors.  ...

### Geometric Properties of the Icosahedral-Hexagonal Grid on the Two-Sphere

Ning Wang, Jin-Luen Lee
2011 SIAM Journal on Scientific Computing
An icosahedral-hexagonal grid on the two-sphere is created by dividing the faces of an icosahedron and projecting the vertices onto the sphere.  ...  This grid and its Voronoi tessellation have several desirable features for numerical simulations of physical processes on the sphere.  ...  The authors thank Drs. Yuanfu Xie and Dezso Devenyi for their insightful discussions and comments, and Drs. Rainer Bleck and John Brown for their suggestions on the presentation of the article.  ...

### TOOLS TO DETERMINE THE DEGREE OF SUSTAINABLE DEVELOPMENT HARMONIZATION FOR INDUSTRIAL CITY

Volodymyr Buriak
2017 Międzynarodowy Zbiór Prac Naukowych "Współpraca Europejska
Great attention was paid to the analysis of models that determine the relationship between sustainable development constituents and the method evaluation of the degree of sustainable development harmonization  ...  This article provides tools to determine the degree of harmonization of sustainable development, in particular economic, environmental and social aspect and realized its practical application to the industrial  ...  Based on the properties of isosceles and an equilateral triangle "ideal values" of components of sustainable development can be defined (Table . 3).  ...

### Fast regocnition of planar non unit distance graphs [article]

Sascha Kurz
2014 arXiv   pre-print
We study criteria attesting that a given graph can not be embedded in the plane so that neighboring vertices are at unit distance apart and the straight line edges do not cross.  ...  Figure 5 : 5 Example of a non unit distance graph. Table 1 : 1 Maximum number of equilateral triangles in an equil. k-gon.  ...  In Table 1 we have listed the maximum area of an equilateral k-gon measured in units of equilateral triangles. (1) .  ...

### PROBLEM DEPARTMENT

E. L. Brown
1912 School Science and Mathematics
Divide a number a into two parts such that the product of the nth power of one and the mth power of the other shall be a maximum. (Solve without the use of calculus.)  ...  On DO construct an equilateral triangle DOC, C and A being on opposite sides of DO, and draw AC. On AC construct the equilateral triangle ACB so as to contain the point 0.  ...

### Systoles in translation surfaces [article]

Corentin Boissy
2022 arXiv   pre-print
We further study the relation between (locally) maximal values of the systole function and the number of shortest saddle connections.  ...  We give a characterization of the maxima of the systole function on a stratum, and give a family of examples providing local but nonglobal maxima on each stratum of genus at least three.  ...  The greatest number of shortest saddle connections of a surface in H(k 1 , . . . , k r ) is equal to r i=1 3(k i + 1) and this number is realized if and only if the surface is a global maximum for the  ...

### Weak Matching Points with Triangles [article]

Fatemeh Panahi, Ali Mohades, Mansoor Davoodi, Marzieh Eskandari
2021 figshare.com
The problem is to find the maximum car- dinality matching of the points using equilateral trian- gles such that each triangle contains exactly two points and each point lies at most in one triangle.  ...  In this paper, we study the weak point matching prob- lem for a given set of n points and a class of equilateral triangles.  ...  Acknowledgments This research was started at the third Winter School on Computational Geometry organized by the members of the Laboratory of Algorithms and Computational Geometry of Amirkabir University  ...

### Weak Matching Points with Triangles

Fatemeh Panahi, Ali Mohades, Mansoor Davoodi, Marzieh Eskandari
2011 Zenodo
The problem is to find the maximum car- dinality matching of the points using equilateral trian- gles such that each triangle contains exactly two points and each point lies at most in one triangle.  ...  In this paper, we study the weak point matching prob- lem for a given set of n points and a class of equilateral triangles.  ...  Acknowledgments This research was started at the third Winter School on Computational Geometry organized by the members of the Laboratory of Algorithms and Computational Geometry of Amirkabir University  ...

### MAXIMA AND MINIMA AREAS IN GEOMETRY

Otto Dunkel
1928 School Science and Mathematics
But there is no proof given that this condition of equal sides is sufficient to guarantee a maximum area, i. e., that the equilateral triangle has a greater area than any other triangle which satisfies  ...  Of all triangles circumscribed about a circle of given radius r, the one which is equilateral has the smallest perimeter and the smallest area.  ...

### Weak Matching Points with Triangles

Fatemeh Panahi, Ali Mohades, Mansoor Davoodi, Marzieh Eskandari
2011 Canadian Conference on Computational Geometry
The problem is to find the maximum cardinality matching of the points using equilateral triangles such that each triangle contains exactly two points and each point lies at most in one triangle.  ...  In this paper, we study the weak point matching problem for a given set of n points and a class of equilateral triangles.  ...  Acknowledgments This research was started at the third Winter School on Computational Geometry organized by the members of the Laboratory of Algorithms and Computational Geometry of Amirkabir University  ...

### Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami [chapter]

Tetsuo Ida, Hidekazu Takahashi, Mircea Marin, Fadoua Ghourabi, Asem Kasem
2006 Lecture Notes in Computer Science
We present an origami construction of a maximum equilateral triangle inscribed in an origami, and an automated proof of the correctness of the construction.  ...  The cylindrical algebraic decomposition is indispensable to the automated proof of the maximality since the specification of this property involves the notion of inequalities.  ...  A straightforward method to construct an equilateral triangle is to use one of the sides of the origami as a side of an equilateral triangle.  ...

### Packing 16, 17 or 18 circles in an equilateral triangle

J.B.M. Melissen, P.C. Schuur
1995 Discrete Mathematics
We present new, efficient packings for 16, 17 and 18 congruent circles in an equilateral triangle.  ...  The results have been found by the use of simulated annealing and a quasi-Newton optimization technique, supplemented with some human intelligence.  ...  However, in view of the large number of constraints, we prefer a different approach, namely the form maximize min (xi --X j) 2 -'b (Yi -yj)2 i,j=1,2 ..... n,i>j subject to x/~+y2~< 1, i= 1,2 ..... n.  ...

### 193

F. P. Matz, G. B. M. Zerr, J. Scheffer, A. H. Holmes
1905 The American mathematical monthly
The semi-circle inscribed in the equilateral triangle will be projected into the maximum semi-ellipse that can be inscribed in the isosceles triangle, and one of its semi-axes will have the same proportion  ...  Then the radius of the semi-circle will be av which is one-half the perpendicular of the equilateral triangle.  ...
« Previous Showing results 1 — 15 out of 18,046 results