Definitions for magic square
mag·ic square

Princeton's WordNetRate this definition:5.0 / 1 vote

1. magic squarenoun

   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

WiktionaryRate this definition:0.0 / 0 votes

1. magic squarenoun

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

2. magic squarenoun

   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.

WikipediaRate this definition:0.0 / 0 votes

1. Magic square

   In 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 diagonals are the same. The 'order' of the magic square is the number of integers along one side (n), and the constant sum is called the 'magic constant'. If the array includes just the positive integers 1 , 2 , . . . , n 2 {\displaystyle 1,2,...,n^{2}} , the magic square is said to be 'normal'. Some authors take magic square to mean normal magic square.Magic squares that include repeated entries do not fall under this definition and are referred to as 'trivial'. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant this gives a semimagic square' (sometimes called orthomagic square). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. Although completely general methods for producing all the magic squares of all orders do not exist, historically three general techniques have been discovered: by bordering method, by making composite magic squares, and by adding two preliminary squares. There are also more specific strategies like the continuous enumeration method that reproduces specific patterns. Magic squares are generally classified according to their order n as: odd if n is odd, evenly even (also referred to as "doubly even") if n is a multiple of 4, oddly even (also known as "singly even") if n is any other even number. This classification is based on different techniques required to construct odd, evenly even, and oddly even squares. Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on. More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares. Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge. The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century. Magic squares have a long history, dating back to at least 190 BCE in China. At various times they have acquired occult or mythical significance, and have appeared as symbols in works of art. In modern times they have been generalized a number of ways, including using extra or different constraints, multiplying instead of adding cells, using alternate shapes or more than two dimensions, and replacing numbers with shapes and addition with geometric operations.

ChatGPTRate this definition:0.0 / 0 votes

1. magic square

   A magic square is a square arrangement of numbers, usually positive integers, such that the sum of the numbers in each row, each column, and both main diagonals is the same, known as the magic constant. The order of a magic square is the number of cells on each side, and it can be of any size, from 1x1 to infinity. The smallest nontrivial case, order 3, is a square array of the numbers 1 to 9.

WikidataRate this definition:0.0 / 0 votes

1. 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

Matched Categories

1. • Square Matrix

How to pronounce magic square?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say magic square in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of magic square in Chaldean Numerology is: 3

2. Pythagorean Numerology

   The numerical value of magic square in Pythagorean Numerology is: 6

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=magic square
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Magic_Square
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Magic_Square
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=magic square