Magic square

related topics
{math, number, function}
{god, call, give}
{township, household, population}
{@card@, make, design}
{style, bgcolor, rowspan}
{work, book, publish}
{area, community, home}
{specie, animal, plant}
{game, team, player}
{math, energy, light}
{church, century, christian}
{country, population, people}

In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.[1] A normal magic square contains the integers from 1 to n2. The term "magic square" is also sometimes used to refer to any of various types of word square.

Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial, consisting of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3.

The constant sum in every row, column and diagonal is called the magic constant or magic sum, M. The magic constant of a normal magic square depends only on n and has the value

For normal magic squares of order n = 3, 4, 5, ..., the magic constants are:


Full article ▸

related documents
Transposition cipher
Cauchy–Schwarz inequality
Trace (linear algebra)
Locally compact space
Division (mathematics)
Rice's theorem
String (computer science)
Logical connective
Brute-force search
Miranda (programming language)
Ideal (ring theory)
Abel–Ruffini theorem
Natural logarithm
Power series
Preadditive category
Convergence of random variables
J (programming language)
Merge sort
Axiom schema of specification
Splay tree
Euler–Mascheroni constant
Normed vector space
Constructivism (mathematics)
Universal property
Poincaré conjecture
Projective plane
Self-organizing map