Magic Squares

  • The creative team
  • Generating Magic Squares
Professor Edward Brumgnach

This web site generates Magic Squares using the Γ+2 (gamma plus two) method for odd order magic squares (developed by Edward Brumgnach), the Brumgnach-Strachey method for singly even magic squares, and the Durer method for doubly even order magic squares. After the square has been successfully generated it is displayed in a separate window. Any error messages will be displayed in a popup window.

Professor Edward Brumgnach

Mike Metaxas Steve Trowbridge

For more information:
Read the paper on magic squares.
Watch an online presentation on magic squares.

Javascript Code & Website Design:
Assistant Professor Mike Metaxas (Left)
Adjunct Lecturer Steven Trowbridge (Right)

Generating Magic Squares

To generate your very own Magic Square change the Square Size, the First Number, the Gamma Increment and the Plus2 Increment.

Square Size:
First Number:
Gamma Increment:
Plus2 Increment:

Definitions and Formulas for predicting the Magic Sum:
M=order(size);F=First number; GI=Gamma Increment; PI=Plus two Increment.
Pure Sum (when F=1, GI=1, PI=1) = (1/2)(M)(M2 + 1):
FT = First Number Total = M(F-1):
CT = 1+2+...+M:
GIT = Gamma Increment Total = (CT-M){M(GI-1)}:
PIT = Plus2 Increment Total = = (CT-M)(PI-1):
SET = Singly Even Total = (M*M/2)(PI-GI) for singly even, 0 otherwise:
Calculated Magic Sum = PS + FT + GIT + PIT + SET: