Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Kobon_triangle_problem> ?p ?o. }
Showing items 1 to 37 of
37
with 100 items per page.
- Kobon_triangle_problem abstract "The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N(k) of nonoverlapping triangles whose sides lie on an arrangement of k lines. Variations of the problem consider the projective plane rather than the Euclidean plane, and require that the triangles not be crossed by any other lines of the arrangement.Saburo Tamura proved that the largest integer not exceeding k(k − 2)/3 provides an upper bound on the maximal number of nonoverlapping triangles realizable by k lines. In 2007, a tighter upper bound was found by Johannes Bader and Gilles Clément, by proving that Tamura's upper bound couldn't be reached for any k congruent to 0 or 2 (mod 6). The maximum number of triangles is therefore one less than Tamura's bound in these cases. Perfect solutions (Kobon triangle solutions yielding the maximum number of triangles) are known for k = 3, 4, 5, 6, 7, 8, 9, 13, 15 and 17. For k = 10, 11 and 12, the best solutions known reach a number of triangles one less than the upper bound.Given a perfect solution with k0 lines, other Kobon triangle solution numbers can be found for all ki-values whereby using the procedure by D. Forge and J. L. Ramirez Alfonsin. For example, the solution for k0 = 3 leads to the maximal number of nonoverlapping triangles for k = 3,5,9,17,33,65,...".
- Kobon_triangle_problem thumbnail Kobon_triangles.gif?width=300.
- Kobon_triangle_problem wikiPageExternalLink ?page=other.php.
- Kobon_triangle_problem wikiPageID "11391440".
- Kobon_triangle_problem wikiPageRevisionID "544810724".
- Kobon_triangle_problem hasPhotoCollection Kobon_triangle_problem.
- Kobon_triangle_problem subject Category:Discrete_geometry.
- Kobon_triangle_problem subject Category:Recreational_mathematics.
- Kobon_triangle_problem subject Category:Triangles.
- Kobon_triangle_problem subject Category:Unsolved_problems_in_mathematics.
- Kobon_triangle_problem type Abstraction100002137.
- Kobon_triangle_problem type Attribute100024264.
- Kobon_triangle_problem type Condition113920835.
- Kobon_triangle_problem type Difficulty114408086.
- Kobon_triangle_problem type Figure113862780.
- Kobon_triangle_problem type PlaneFigure113863186.
- Kobon_triangle_problem type Polygon113866144.
- Kobon_triangle_problem type Problem114410605.
- Kobon_triangle_problem type Shape100027807.
- Kobon_triangle_problem type State100024720.
- Kobon_triangle_problem type Triangle113879320.
- Kobon_triangle_problem type Triangles.
- Kobon_triangle_problem type UnsolvedProblemsInMathematics.
- Kobon_triangle_problem comment "The Kobon triangle problem is an unsolved problem in combinatorial geometry first stated by Kobon Fujimura. The problem asks for the largest number N(k) of nonoverlapping triangles whose sides lie on an arrangement of k lines.".
- Kobon_triangle_problem label "Kobon triangle problem".
- Kobon_triangle_problem label "Kobon-Dreiecke".
- Kobon_triangle_problem label "Triangle de Kobon".
- Kobon_triangle_problem label "藤村幸三郎的三角形問題".
- Kobon_triangle_problem sameAs Kobon-Dreiecke.
- Kobon_triangle_problem sameAs Triangle_de_Kobon.
- Kobon_triangle_problem sameAs m.02r9xgm.
- Kobon_triangle_problem sameAs Q1269124.
- Kobon_triangle_problem sameAs Q1269124.
- Kobon_triangle_problem sameAs Kobon_triangle_problem.
- Kobon_triangle_problem wasDerivedFrom Kobon_triangle_problem?oldid=544810724.
- Kobon_triangle_problem depiction Kobon_triangles.gif.
- Kobon_triangle_problem isPrimaryTopicOf Kobon_triangle_problem.
