magic square

Thân thiện

A student draws a magic square on the chalkboard.

Definition

Noun: A magic square is a square grid (a matrix) containing n rows and n columns. It is filled with the first n² positive integers (1, 2, 3, ..., n²), arranged so that the sum of the numbers in any row, any column, and both main diagonals is the same constant value. This constant is known as the magic constant.

Usage

The term "magic square" is used as a countable noun to describe this specific mathematical arrangement. * The ancient Chinese *Lo Shu square is a famous 3x3 magic square.* * Creating a magic square of an even order is more complex than for an odd order. * The puzzle involved completing the missing numbers in the magic square.

Advanced Usage

• Normal Magic Square: The most common type, using consecutive integers starting from 1.
• Magic Constant/Sum: The identical sum produced by each row, column, and diagonal. For a normal magic square of order , the magic constant is .
• Order of a Magic Square: Refers to the number of cells on one side (). A 4x4 square is of order 4.
• Pandiagonal Magic Square: A special type where the broken diagonals (wrapping around the edges) also sum to the magic constant.

Variants and Related Words

• Semi-Magic Square: A square where the rows and columns sum to the same constant, but the diagonals do not.
• Magic Cube: The three-dimensional analogue of a magic square.
• Latin Square: A different combinatorial square grid where each symbol appears once in each row and column.

Synonyms

• Mathematical Square (This is a broader, less precise term)
• Number Square (General term; not all number squares are magic squares)

Related Phrases

• To construct a magic square: To create or build one.
  • Algorithms exist to construct a magic square of any size.
• To solve a magic square: To find the missing numbers in an incomplete one.
  • The challenge was to solve the 5x5 magic square.

Học thuật

Noun

1. 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