Magic Square Patterns

Extract

Diagrammatic methods may be used to establish some well known facts about magic squares

In a magic square with 9 cells, the number in the central cell is always a, the average of the three numbers in each row, column or diagonal. Using a dot to represent the number in any cell, fill the cells of a 3 × 3 square in this way: put a dot in each of the cells forming a diagonal: these dots represent numbers totalling 3a.