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These extended lines can also be interpreted as normal lines through an infinite grid in the Euclidean plane, taken modulo the dimensions of the torus. For a torus based on an m × n {\displaystyle m\times n} grid, the maximum number of points that can be chosen with no three in line is at most 2 gcd ( m , n ) {\displaystyle 2\gcd(m,n)} . [ 25 ]
In geometry, a tetrad is a set of four simply connected disjoint planar regions in the plane, each pair sharing a finite portion of common boundary. It was named by Michael R. W. Buckley in 1975 in the Journal of Recreational Mathematics .
In 1867, in the French chess journal Le Sphinx, an intellectual precursor to the nine dots puzzle appeared credited to Sam Loyd. [1] [2] Said chess puzzle corresponds to a "64 dots puzzle", i.e., marking all dots of an 8-by-8 square lattice, with an added constraint. [a] The Columbus Egg Puzzle from The Strand Magazine, 1907
Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.
Animation of the missing square puzzle, showing the two arrangements of the pieces and the "missing" square Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid. The missing square puzzle is an optical illusion used in mathematics classes to help students ...
This puzzle can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph,, with vertices representing the houses and utilities and edges representing their connections, has a graph embedding in the plane. The impossibility of the puzzle corresponds to the fact that , is not a planar graph.
A conformal map acting on a rectangular grid. Note that the orthogonality of the curved grid is retained. While vector operations and physical laws are normally easiest to derive in Cartesian coordinates, non-Cartesian orthogonal coordinates are often used instead for the solution of various problems, especially boundary value problems, such as those arising in field theories of quantum ...
A completed nonogram of the letter "W" from the Wikipedia logo. Nonograms, also known as Hanjie, Paint by Numbers, Picross, Griddlers, and Pic-a-Pix, are picture logic puzzles in which cells in a grid must be colored or left blank according to numbers at the edges of the grid to reveal a hidden picture.