A Visit to the Square

Published on Thursday, May 28, 2009 in , , , , , , ,

Double Birthday Magic Square“Although it's difficult for us ‘math guys’ to appreciate, the vast majority of the population (here and elsewhere) has neither heard of a ‘magic square’ nor is aware of its properties. So the entertainment aspect of presenting same is inherent in its surprise value, as the audience is brought to realize the truly amazing number of ways in which this hastily constructed set of numbers can be summed to create the ‘magic number’.”
-Doug Dyment

It seems like too long to me since I last discussed magic squares, and it seems like magic square resources have been jumping out at me recently, so it seems to be the right time.

First, there's the classic W. S. Andews book, Magic Squares and Cubes (PDF), which is now available in the public domain. If you've ever wanted to study the magic square (and/or the magic cube) in depth, you'll find this work very satisfying.

On a briefer level, Curious Math offers several excellent, and easily-digestible, magic square lessons. I especially enjoy the look at the thought process behind the creation of the standard 3-by-3 magic square.

For those of you who've tried learning the magic square here on Grey Matters, there are some further help on helping memorize the required numbers. There are even some alternative approaches here that you may find quicker, depending on your particular approach to learning. I've included a permanent link to this discussion in my tutorial itself, as well.

Even when you get a magic square method down, there still remains the question of presentation. Traditionally, there have been 2 standard approaches to the square. In the first, you openly ask for the number, and quickly generate a magic square for that number. This option gives a Rain Man-type feel, and it can be tough for the performer to overcome the “show-off” perception by the audience.

The other standard magic square presentation is that of having a spectator choose a number and keep it secret, and then creating a square, after somehow secretly obtaining the number. The nice thing about this is that the magic square doesn't really communicate what relationship it has to the chosen number until you reveal the patterns. It has good potential for comedy, drama and or mysticism, and when done well, seems much less like a stunt.

These aren't the only possible presentations, however. In Subliminal Squares, for example, you create a magic square, and then demonstrate that a an audience member's mind has been invaded subconsciously by the magic total!

One way to make the magic square more meaningful to an audience is to use a meaningful number or total, such as someone's birthday. Professor Arthur Benjamin, back in 2006, published a means of generating what he calls the Double Birthday Magic Square (PDF), which has recently been made available on his site. The magic square that's created features the spectator's birthday both across the top and in the 4 corners! As it happens, this method works very well with the presentation I first discussed in my Plots For Memory Routines post.

To wind up this magic square post, enjoy Benji Bruce's take on the magic square. He grabs interest by performing it as if it were being done at a poetry slam:

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3 Response to A Visit to the Square

5:34 PM

Hello again, Just wanted you to know that I have found another great site about magic squares for your collection. This one has a version where you can let three audience members give you three numbers to start off with. Here's the link

p.s. I love doing Dr. Benjamin's birthday square for people on their birthday. A special treat I use to unleash the moment. Keep up the great site,

12:19 PM

Me again,

I just realized that the link I provided doesn't work for some reason. Here is a link to their main page, sorry.



11:18 AM


something new in the world ... physical aspects of magic squares