a list compiled by Alex Kasman (College of Charleston)

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Magic Squares (1977)
Paul Calter

Contributed by Vijay Fafat

A very unconventionally written mystery story full of well placed and well-integrated problems in mathematics, which makes this a great book to be included in a course on ‘mathematics in literature’. The book may remind one of some of those by Clifford Pickover. However, unlike the other books which are very loose, even contrived settings which are rendered not for their fictional / literary value but to showcase the main subject matter of serious and interesting Physics or Mathematics, Calter’s book is really a creative mystery for 6th - 7th graders, with interesting juxtaposition of problems into which older children can sink their teeth. For example, at one point in the story, the hero is trapped in a tunnel, with an escape route and a long, heavy beam lying on the floor available. However, to escape, he has to manoeuvre the beam around a 90-degree turn. He has to decide quickly if the beam can fit the corner turn before trying to move it, since he is running out of time. Knowing the dimensions of the tunnel and the beam, he calculates and answer with a little geometry. The reader is then asked to show the same calculations.

There are quite a few such problems set for the reader, many of which are also asked to be written down as computer programs (A sampling appears below.) Mathematical concepts like Perfect Numbers, Pythagorean numbers, factorials, magic squares, combinatorics, logarithmic spiral, golden mean, definite integrals, etc are woven into the story. The characters in the mystery have mathematical names, like Matrix Inverse (hero), Sebastian Sinusoid (villain), Priscilla Prime (hero’s flame), Radian, Arclet, etc. (all the math puns in the book reminded me of Ian Stewart’s “Flattterland”). And then there are these computer commands which are printed on every page, almost at random. I could not figure out if there was any specific purpose to them or if they were simply a quirky add-on (it would have been great if they had formed a sub-plot of their own, when taken together).

A few problems paraphrased from the book:

  1. Fill in the magic square in the story to break the code. You need to know that for an n by n magic square, the magic square constant is n*(n^2+1)/2
  2. Compute the lengths of two radii on a logarithmic spiral and show that they are in golden ratio (the problem appears to be incomplete)
  3. Evaluate the integrals for functions exp(x) and cos(x)^2+9 between 0 and 10 to solve the deed puzzle Write a program to generate prime numbers.
  4. Write a program which gives the sum of the digits of any number. Verify that nine is a circular number as defined in the story.
  5. Write a program to find the prime factors of any integer. There is a lovely reference to billiards on an elliptical table, where the villain proceeds to clear out the table with ease. As the text says,

    (quoted from Magic Squares)

    “It was not difficult, for the table was in the shape of an ellipse. There was only one pocket, located at a foocal point, while the other focal point was marked with a white spot. He had only to hit a ball so that it crossed the spot, and it would reach the pocket after bouncing off the elliptical cushion”

    Oh, and the story itself. A familiar theme of a super-villain, head of the organization called “Numeranarchists”, who wants to blow up the world – or in this case, wants civilization to give up computers. He starts creating random malfunctions in the computers world-wide and gives progressively direr warnings to the world to stop using them. He nearly succeeds, till he fails – to borrow Yogi Berra.

(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to Magic Squares
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. Math Patrol by TV Ontario
  2. Mathmakers by TV Ontario
  3. Evil Genius by Catherine Jinks
  4. Odd Squad by Tim McKeon / Adam Peltzman
  5. Donald in Mathmagic Land by Hamilton Luske (director)
  6. Math Curse by Jon Scieszka / Lane Smith (illustrator)
  7. The Cat in Numberland by Ivar Ekeland (author) / John O'Brien (illustrator)
  8. A Tangled Tale by Lewis Carroll
  9. The Magic Two-Horn by Sergey Pavlovich Bobrov
  10. The Number Devil (Der Zahlenteufel) by Hans Magnus Enzensberger
Ratings for Magic Squares:
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GenreHumorous, Didactic, Children's Literature, Adventure/Espionage,
TopicReal Mathematics,

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(Maintained by Alex Kasman, College of Charleston)