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Magic Hexagon
A magic hexagon of order ''n'' is an arrangement of numbers in a centered hexagonal number, centered hexagonal pattern with ''n'' cells on each edge, in such a way that the numbers in each row, in all three directions, sum to the same magic constant ''M''. A normal magic hexagon contains the consecutive integers from 1 to 3''n''2 − 3''n'' + 1. Normal magic hexagons exist only for ''n'' = 1 (which is trivial, as it is composed of only 1 cell) and ''n'' = 3. Moreover, the solution of order 3 is essentially unique. Meng gives a less intricate constructive mathematical proof, proof.Meng, F"Research into the Order 3 Magic Hexagon" ''Shing-Tung Yau Awards'', October 2008. Retrieved on 2009-12-16. The order-3 magic hexagon has been published many times as a 'new' discovery. An early reference, and possibly the first discoverer, is Ernst von Haselberg (1887). Proof of normal magic hexagons The numbers in the hexagon are consecutive, and run fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagonal Tortoise Problem
The hexagonal tortoise problem () was invented by Korean aristocrat and mathematician Choi Seok-jeong (1646–1715). It is a mathematical problem that involves a hexagonal lattice, like the hexagonal pattern on some tortoises' shells, to the (''N'') vertices of which must be assigned integers (from 1 to ''N'') in such a way that the sum of all integers at the vertices of each hexagon is the same. The problem has apparent similarities to a magic square In mathematics, especially History of mathematics, historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diago ... although it is a vertex-magic format rather than an edge-magic form or the more typical rows-of-cells form. His book, ''Gusuryak'', contains many mathematical discoveries. References Sources used * Magic figures {{numtheory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parity (mathematics)
In mathematics, parity is the Property (mathematics), property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not.. For example, −4, 0, and 82 are even numbers, while −3, 5, 23, and 69 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers with decimals or fractions like 1/2 or 4.6978. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon 9 Gradient Solution Pure 200
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A regular hexagon is defined as a hexagon that is both equilateral and equiangular. In other words, a hexagon is said to be regular if the edges are all equal in length, and each of its internal angle is equal to 120°. The Schläfli symbol denotes this polygon as \ . However, the regular hexagon can also be considered as the cutting off the vertices of an equilateral triangle, which can also be denoted as \mathrm\ . A regular hexagon is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed circle). Measurement The longest diagonals of a regu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
