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In geometry, the rhombille tiling, [1] also known as tumbling blocks, [2] reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets ...
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.
Four-sided dice were among the gambling and divination tools used by early man who carved them from nuts, wood, stone, ivory and bone. [2] Six-sided dice were invented later but four-sided dice continued to be popular in Russia. In Ancient Rome, elongated four-sided dice were called tali while the six-sided cubic dice were tesserae. [3]
Computational origami results either address origami design or origami foldability. [3] In origami design problems, the goal is to design an object that can be folded out of paper given a specific target configuration. In origami foldability problems, the goal is to fold something using the creases of an initial configuration.
Five dice showing 41,256, which denotes "monogram" on an updated EFF cryptographic word list. Diceware is a method for creating passphrases, passwords, and other cryptographic variables using ordinary dice as a hardware random number generator. For each word in the passphrase, five rolls of a six-sided die are required.
This gives us the distribution of spots on the faces of a pair of Sicherman dice as being {1,2,2,3,3,4} and {1,3,4,5,6,8}, as above. This technique can be extended for dice with an arbitrary number of sides.
Of the cleanly formulated Hilbert problems, numbers 3, 7, 10, 14, 17, 18, 19, 21, and 20 have resolutions that are accepted by consensus of the mathematical community. Problems 1, 2, 5, 6, [a] 9, 11, 12, 15, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems.
For odd square, since there are (n - 1)/2 same sided rows or columns, there are (n - 1)(n - 3)/8 pairs of such rows or columns that can be interchanged. Thus, there are 2 (n - 1)(n - 3)/8 × 2 (n - 1)(n - 3)/8 = 2 (n - 1)(n - 3)/4 equivalent magic squares obtained by combining such interchanges. Interchanging all the same sided rows flips each ...