Home > Challenge, Geometry > Geomagic Squares

Geomagic Squares

The magic square is an ancient and well-known mathematical object.  In the figure at the right, the sum of every row, column, and diagonal is the same, namely, 30.  This is a basic magic square.

Magic squares have been around for thousands of years, and there many variations have been explored.  Which makes the invention of a new kind of magic square all the more amazing:  the geomagic square.


These geomagic squares turn the algebraic magic square into something geometrical:  instead of numbers summing up to the magic constant in every direction, polygonal tiles can be put together to form the same shape in every direction!  Here’s an example.

With some flipping and rotating, every sequence of tiles in this “square” can be arranged to make the same figure, namely, a 4 x 4 square with one small square missing. The example at the right shows the middle row being assembled to form the “magic constant”:  the white square in the middle is the missing square.

The natural questions:  how do you construct geomagic squares?  Can you make a geomagic square for any given “magic constant”?  For a given magic constant“, how many geomagic squares can you create?  What others can you think of? 

Click here to see more in Geometry.


  1. No comments yet.
  1. No trackbacks yet.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: