You're probably wondering why I'm reviewing three books in one post. All three are concerned with magic square routines, and there's also been some mingling of influence among the books.
In addition, they all came to my attention nearly simultaneously. In fact, the author e-mailed me and offered to send me review copies of their books literally within minutes of each other.
IntroductionAll three of these books work to counter common problems with many magic squares. The first magic square routine most performers learn is similar to the Instant Magic Square I teach over in the Mental Gym.
Using numbers that are too low can result in duplicate numbers. Using numbers that are too high, as I've previously discussed in my post about Bill Fritz' free notes/screencasts, Magic Squares for the Mathematically Challenged, can result in numbers that expose the pattern by being in a different range than the others.
Stigma SquareNico Reuter's book, Stigma Square is focused on a birthday square presentation. Most such routines place the month in one square, the date in another square, and then split the 4-digit year up between 2 squares. Stigma Square's difference is that only the month and the date are placed in individual magic square cells, and the year is the magic total!
In the approaches where the year is in the magic square itself, the magic total is simply the sum of the numbers involved, so the total itself often has no relevance. Nico's approach makes the magic square more satisfying, as the starting point AND ending point are all relevant to the spectator's birthday. This also helps the routine feel more complete, from an audience standpoint.
The name Stigma Square comes from another unusual approach used here. Before the spectator is asked for their birthday, they're given a folded piece of paper, and told not to look at it for the time being. After the birthday is given, and the magic square created, the performer shows how all the various combinations add up to year the spectator was born, until he runs across some that don't match the year.
At this point, the performer reminds the spectator about the piece of paper given earlier. The piece of paper is shown to contain one more number, which is added to the magic square, and resolves the dilemma perfectly. The performer can then show further combinations that give the spectator's birth year. This twist is a nice take on the magician-in-trouble syndrome, and helps add drama.
The notes themselves are very clear, and take the reader clearly through each step. Once the square itself is explained, then the basic presentation is explained. The main presentation is focused on the speed with which the square is developed. There is an alternate presentation, based on a Doug Dyment idea, in which the square is developed more slowly, with spectators following each step in detail, and experiencing smaller moments of amazement that build up to the end.
The math involved isn't complex, and Nico clearly explains how to deal with even the largest numbers in a manner simple enough to do in your head. Not only are credits and references given as appropriate, but references to especially interesting routines for further reading are given throughout the book.
There's also a non-magic square bonus effect with a man-vs-calculator presentation that would make a good opener. The method is subtle, involves no sleight of hand, and went right past me until I read the method.
Nico has done a first run of only 50 copies, and only sells it directly. If you're interested, you can e-mail him about pricing and availablity at firstname.lastname@example.org.
E-Z Square 3The Werner Miller's E-Z Square book series is focused on teaching techniques, with less emphasis on presentation.
E-Z Square 3 concerns creating 4 by 4 magic squares in which the four corners or four center squares are given by the audience. These two techniques are taught separately, with detailed step-by-step illustrations, and simple graphics showing the arrangements that give the magic total.
Of the two approaches, a little experimentation has given me a preference for starting with the four center squares, as the pattern feels simple and more direct. For each reader, however, this will be a personal choice.
Also, variations of both techniques are taught. Besides starting with four given numbers, you can start with a given total, or even two given numbers and a total!
Starting with two given numbers and a magic total is also the starting point of Stigma Square, with which Werner Miller is familiar. In E-Z Square 3, he teaches a different way of creating a Stigma Square, including an alternative number placement and ending.
You might expect the teaching of a magic square to be hard to understand, but the clarity of the illustrations makes each step easy to grasp. Short of animating the illustrations, it's hard to see how to make them any clearer. Those concerned about the lack of a specific presentation shouldn't worry, as there are enough ideas to spark anyone's creativity, and get them thinking about their own unique presentation.
When it comes to the creation of the Stigma Square specifically, choosing between the two approaches will be up to each performer. Werner Miller's approach is more visual, while Nico's has a procedural rhythm to it.
E-Z Square 3, by Werner Miller, is available from Lybrary.com. That version is in English, and a German edition is also available.
E-Z Square 4Even when you're accustomed to the rest of the E-Z Square series, E-Z Square 4 can seem a little unusual at first.
The first routine in this book is Détour Square, in which the audience gives you four numbers to place in the top row. The remaining squares are filled out quickly, but only the rows and columns add to the same total. The diagonals give a different sum.
The performer then takes the same numbers and copies them into different locations on a second grid, and this time the rows, columns, AND diagonals all give the same total! This is quite a different take on the magic square, and its impressive that the magician can be restricted to the same numbers, yet still be able to develop an arrangement that improves on the original!
With an understanding of the first routine, the second routine, dubbed Direttissima shows how to achieve a similar resulting square in one step. Because of the wider varieties of arrangements possible with the first version, as well as the theatrical interest generated by the presentation, the Détour Square remains the more powerful of the two.
In the previously-mentioned Magic Squares for the Mathematically Challenged, Bill Fritz uses a presentation where he quickly writes down each number on a different Post-It Note, and stick them on the wall. He then takes a look at them, and re-arranges them as if a pattern is occurring to him. The ease of Werner Miller's method combined with the freedom of movement of Bill Fritz' presentation work quite nicely together.
The hallmark of all the E-Z Square is their clarity of magic square instruction, as well as a selection of variations that's enough to start your mind racing with presentational possibilities.
E-Z Square 4 closes with a bonus effect which combines puzzles, geometry, and magic squares in a way that can even fool the person performing the routine.
Like the rest of the series, Werner Miller's E-Z Square 4 is also available from Lybrary.com, and is available in German.
Closing ThoughtsIf you think that the only possibilities for magic square presentations are the look how smart I am, or How fast can I do this? variety, any or all of these books can give you a whole new respect for the genre. The magician-in-trouble aspect hasn't been used much in magic squares, and it's good to see these and other possibilities opened up.
If you're at all interested in performing magic squares, these 3 books are well worth the investment.