Filters








215,434 Hits in 3.4 sec

On smallest triangles [article]

Geoffrey Grimmett, Svante Janson
2002 arXiv   pre-print
It is proved in addition that, if mu is the uniform probability measure on the region S, then c(mu) <= 2/|S|, where |S| denotes the area of S.  ...  This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle.  ...  Some of this work was done at Eurandom, during the attendance by the authors at a meeting on discrete probability. David Stirzaker kindly indicated the relevance of the work of Morgan Crofton.  ... 
arXiv:math/0208044v1 fatcat:vnvxp4fhwrbufmruj7vh3oeteu

On smallest triangles

Geoffrey Grimmett, Svante Janson
2003 Random structures & algorithms (Print)  
It is proved in addition that, if µ is the uniform probability measure on the region S, then κ(µ) ≤ 2/|S|, where |S| denotes the area of S.  ...  This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle.  ...  Some of this work was done at Eurandom, during the attendance by the authors at a meeting on discrete probability. David Stirzaker kindly indicated the relevance of the work of Morgan Crofton.  ... 
doi:10.1002/rsa.10092 fatcat:q3bko4snlvarrepgdekztpc7ku

Largest and Smallest Area Triangles on Imprecise Points [article]

Vahideh Keikha, Maarten Löffler, Ali Mohades
2018 arXiv   pre-print
smallest triangle is NP-hard; but minimizing the smallest triangle can be done in O(n^2) time.  ...  Assume we are given a set of parallel line segments in the plane, and we wish to place a point on each line segment such that the resulting point set maximizes or minimizes the area of the largest or smallest  ...  Consequently the smallest largest-area triangle of L equals to the smallest largest-area triangle of L .  ... 
arXiv:1712.08911v2 fatcat:t52s7h7o2rc3fpbgsvi7ouj4xi

The smallest triangular cover for triangles of diameter one

Liping Yuan, Ren Ding
2005 Journal of Applied Mathematics and Computing  
In this paper, we find the smallest triangular cover of any prescribed shape for the family S of all triangles of diameter 1.  ...  A convex region covers a family of curves if it contains a congruent copy of each curve in the family, and a "worm problem" for that family is to find the convex region of smallest area.  ...  Now, we present our main results on the smallest triangular cover, denoted as T , of prescribed shape for triangles of diameter one. Theorem 1.  ... 
doi:10.1007/bf02936039 fatcat:rxo3krjfrnfornf23w5pfjqay4

On a smallest topological triangle free (n_4) point-line configuration

Jürgen Bokowski, Hendrik Van Maldeghem
2020 The Art of Discrete and Applied Mathematics  
An (n k ) configuration is a set of n points and n lines such that every point lies on precisely k of these lines and every line contains precisely k of these points. We distinguish three concepts.  ...  A topological (n 4 ) configuration for n < 40 must contain a triangle, so our triangle free example is minimal. A c c e p t e d m a n u s c r i p t 2 Art Discrete Appl. Math. Definition 1.1.  ...  It is the smallest case for which we do not know a result like the previous theorem, and it is small enough to possibly behave exceptionally.  ... 
doi:10.26493/2590-9770.1355.f3d fatcat:efpioe5wszgvfpeso4muebko2q

ON SMALLEST ORDER OF TRIANGLE-FREE GRAPHS WITH PRESCRIBED (3, k)-DEFECTIVE CHROMATIC NUMBER

Mudin Simanihuruk
2018 Far East Journal of Mathematical Sciences (FJMS)  
Let f(m,k) be the smallest order of a triangle-free graph G such that X k (G) = m. In this paper we study the problem of determining f( m, 1).  ...  A graph is (m,k)-colourable if its vertices can be coloured with m colours such that the maximum degree of the subgraph induced on vertices receiving the same colour is at most k.  ...  Let f(m,k) be the smallest order of a triangle-free graph G such that x'k (G) = m. The determination of f(m,O) is still an open problem (see Toft [19] , Problem 29).  ... 
doi:10.17654/ms103040717 fatcat:xpznpo5afrge7kb72pq3h7jvli

AN OPTIMAL PARALLEL ALGORITHM FOR FINDING THE SMALLEST ENCLOSING TRIANGLE ON A MESH-CONNECTED COMPUTER∗

JUNG-JU CHOI, CHANG-SUNG JEONG, MYUNG-SOO KIM
1993 Parallel Algorithms and Applications  
In this paper, we consider the problem of nding the smallest triangle circumscribing a convex polygon with n edges.  ...  Since the nontrivial operation on MCC requires ( p n), the time complexity is optimal within constant time factor.  ...  , and nd the smallest one among all the P-anchored triangles.  ... 
doi:10.1080/10637199308915435 fatcat:jqgarbcvtjduvpjry6c6gehkue

Fitting triangle into regular octagon

Banyat Sroysang
2013 Applied Mathematical Sciences  
In this paper, we determine the smallest regular octagon which contains all triangles of perimeter two. Mathematics Subject Classification: 52C15  ...  The Moser's worm problem [2] searches the region of smallest area which contains a congruent copy of every unit arc on the plane. A popular shape of arcs is a triangle.  ...  Results Theorem The smallest regular octagon cover for the family of all triangles of perimeter two is the regular octagon of diameter one (the area is 1 2 ). Proof.  ... 
doi:10.12988/ams.2013.35263 fatcat:6t4hxvw65rc5pekmqzoiam3blu

Regular hexagon cover for isoperimetric triangles

B. Sroysang
2013 Applied Mathematical Sciences  
In this paper, we search for the smallest regular hexagon which covers the family of all triangles of perimeter two.  ...  The Moser's worm problem [2] searches the region of smallest area which contains a congruent copy of every unit arc on the plane. A popular shape of arcs is a triangle.  ...  In 2009, Zhang and Yuan [7] gave the smallest regularized parallelogram cover, whose length of the smaller diagonal is not less than one, for the family of all triangles of perimeter two.  ... 
doi:10.12988/ams.2013.13141 fatcat:z5j74kiq5bgu5jykmql3acq43q

Lepp terminal centroid method for quality triangulation

Maria-Cecilia Rivara, Carlo Calderon
2010 Computer-Aided Design  
Longest edge based algorithms [18] [19] [20] 3, 4, 6] were designed to take advantage of the following mathematical properties on the quality of triangles generated by iterative longest edge bisection  ...  smallest edges over the boundary.  ...  Furthermore when the equality on the bound on the largest angle holds for one of the triangles (say triangle ABC), then the other triangle is equilateral, the 4 vertices are cocircular and the distance  ... 
doi:10.1016/j.cad.2008.11.004 fatcat:usgcnqozc5hv7bvnxvgpbhvfi4

Triangles in regular heptagons

B. Sroysang
2013 Applied Mathematical Sciences  
In this paper, we show that the regular heptagon of diameter one is the smallest regular heptagon which contains all triangles of perimeter two. Mathematics Subject Classification: 52C15  ...  In this paper, we show that the regular heptagon of diameter one is the smallest regular heptagon which contains all triangles of perimeter two.  ...  Results Theorem The smallest regular heptagon cover for the family of all triangles of perimeter two is the regular heptagon of diameter one (the area is approximately equal to 0.71974). Proof.  ... 
doi:10.12988/ams.2013.13143 fatcat:6g4ceblryfeopns3lsilk3j6ti

A Study on Size-Optimal Longest Edge Refinement Algorithms [chapter]

Carlos Bedregal, María-Cecilia Rivara
2013 Proceedings of the 21st International Meshing Roundtable  
Until now, these algorithms did not provide theoretical guarantees on the size of the triangulation obtained.  ...  Q on its smallest edge CA.  ...  Refining triangles by the smallest edge When a non-conforming triangle is produced after adding a point on its smallest edge (as described in Case 3 of Sec. 4.1), the triangulation is made valid after  ... 
doi:10.1007/978-3-642-33573-0_8 dblp:conf/imr/BedregalR12 fatcat:tmblm7i22za5hhmkcf6hhvtbxe

90.80 Boxes for triangles of diameter one

Liping Yuan, Yuqin Zhang, Ren Ding
2006 Mathematical Gazette  
Since the equilateral triangle with side length 1 has altitude ^V3, it is easy to see that the breadth of a triangle of diameter one is at most \\J?>.  ...  A 'worm problem' for that family is to find the box of smallest area. Suppose X is a bounded convex set of points in the plane.  ...  Thus R covers every triangle of diameter 1, giving Lemma 1. Now we determine the smallest box for triangles of diameter one.  ... 
doi:10.1017/s0025557200180465 fatcat:cz4gqz4u7jez5ncvhuagon2z5u

Regular pentagon cover for triangles of perimeter two

B. Sroysang
2013 Applied Mathematical Sciences  
Wetzel determined the smallest rectangle which covers the family of all triangles with perimeter two.  ...  In this paper, we search for the smallest right trapezoid which covers the family of all triangles of perimeter two.  ...  However, we can scale between triangles with perimeter one and triangles with perimeter two.  ... 
doi:10.12988/ams.2013.13142 fatcat:cmtheuqgwncrvcarcinzafyf7y

Longest-edge algorithms for size-optimal refinement of triangulations

Carlos Bedregal, Maria-Cecilia Rivara
2014 Computer-Aided Design  
the smallest angle).  ...  We prove that the iterative application of the algorithm gradually reduces the average extent of the propagation per target triangle, tending to affect only two triangles.  ...  In exchange, for non-conforming midpoints situated over the smallest edge of t * , some additional points in the interior and/or over the edges of t * are introduced, depending on the geometric triangle  ... 
doi:10.1016/j.cad.2013.08.040 fatcat:ct4wzt2ymbeffnopqrxf6momx4
« Previous Showing results 1 — 15 out of 215,434 results