Magic square
A square array of numbers in which every row, column, and usually both main diagonals have the same sum, called the magic constant.
Magic constant: The common sum shared by the rows, columns, and required diagonals of a magic square. It is the target sum that every qualifying line must reach.
Linear algebra: The branch of mathematics that studies vectors, matrices, and linear equations. Magic-square conditions form a system of linear equations on the cell entries.
Lo Shu Square: An ancient Chinese three-by-three magic square using the numbers one through nine. It is an early canonical example associated with the tradition's beginnings.
Recreational mathematics: Mathematical problems and activities pursued for curiosity, play, or entertainment. Magic squares are a classic puzzle whose constraints invite systematic construction.
Sudoku: A number-placement puzzle requiring each digit to occur once in every row, column, and subgrid. Sudoku shares row-and-column constraints but does not require equal sums.
Normal magic square: A magic square of order n containing each integer from 1 through n² exactly once. This familiar restricted form makes the entries and their total precise.
Birkhoff polytope: The polytope of doubly stochastic square matrices, whose rows and columns each sum to one. Its row-and-column constraints parallel part of the magic-square equations.
Yang Hui: A Chinese mathematician of the Southern Song dynasty known for writings on mathematics, including magic squares. His work records and develops methods for constructing such squares.
Combinatorial design: A structured arrangement of finite objects satisfying specified balance or incidence conditions. Magic squares exemplify how local constraints create a globally balanced arrangement.
Semimagic square: A square array whose rows and columns have equal sums, without requiring diagonal sums to match. It is the standard near-neighbor when diagonal conditions are omitted.