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The crossed ladders problem may appear in various forms, with variations in name, using various lengths and heights, or requesting unusual solutions such as cases where all values are integers. Its charm has been attributed to a seeming simplicity which can quickly devolve into an "algebraic mess" (characterization attributed by Gardner to D. F ...
In the mathematical field of graph theory, the ladder graph L n is a planar, undirected graph with 2n vertices and 3n – 2 edges. [ 1 ] The ladder graph can be obtained as the Cartesian product of two path graphs , one of which has only one edge: L n ,1 = P n × P 2 .
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
Hertz solved the contact problem in the absence of friction, for a simple geometry (curved surfaces with constant radii of curvature). Carter considered the rolling contact between a cylinder and a plane, as described above. A complete analytical solution is provided for the tangential traction.
When we recently wrote about the toughest math problems that have been solved, we mentioned one of the greatest achievements in 20th-century math: the solution to Fermat’s Last Theorem. Sir ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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This category is intended for all unsolved problems in mathematics, including conjectures. Conjectures are qualified by having a suggested or proposed hypothesis. Conjectures are qualified by having a suggested or proposed hypothesis.