# Definitions for **magic square**

### This page provides all possible meanings and translations of the word **magic square**

### Random House Webster's College Dictionary

mag′ic square′(n.)

a square containing integers arranged in an equal number of rows and columns so that the sum of the integers in any row, column, or diagonal is the same.

**Category:**Math

#### Origin of **magic square**:

1695–1705

### Princeton's WordNet

magic square(noun)

a square matrix of n rows and columns; the first n^2 integers are arranged in the cells of the matrix in such a way that the sum of any row or column or diagonal is the same

### Wiktionary

magic square(Noun)

A palindromic square word arrangement, usually in the form of a magic amulet.

magic square(Noun)

An n-by-n arrangement of n numbers such that the numbers in each row, in each column and along both diagonals all have the same sum.

### Freebase

Magic square

In recreational mathematics, a magic square is an arrangement of numbers in a square grid, where the numbers in each row, and in each column, and the numbers that run diagonally in both directions, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows it has. Thus, a magic square always contains n² numbers, and its size is described as being "of order n". A magic square that contains the integers from 1 to n² is called a normal magic square. It is possible to construct a normal magic square of any size except 2 x 2, although the solution to a magic square where n = 1 is trivial, since it consists simply of a single cell containing the number 1. The smallest nontrivial case, shown below, is a 3 x 3 grid. The constant that is the sum of every row, column and diagonal is called the magic constant or magic sum, M. Every normal magic square has a unique constant determined solely by the value of n, which can be calculated using this formula:²

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"magic square." *Definitions.net.* STANDS4 LLC, 2014. Web. 20 Oct. 2014. <http://www.definitions.net/definition/magic square>.