Chapter 1 Projects

Section 1.2 Individual Research

Individual Research Project 1.2

Write a short paper about the construction of magic squares.



You might include such facts as there is 1 standard magic square of order 1, 0 of order 2, 8 of order 3, 440 of order 4, and 275,305,224 of order 5. According to the Guinness Book of World Records, Leon H. Nissimov of San Antonio, Texas, has discovered the largest known magic square with sum of 999,999,999,989. Show that such a magic square is not possible. You might also include the properties of the magic square discovered by Benjamin Franklin.

Individual Research Project 1.3

Design a piece of art based on a magic square.

A process for producing an artistic pattern using magic squares is described in an article, "An Art-Ful Application Using Magic Squares " by Margaret J. Kenney (The Mathematics Teacher, January 1982, pp. 83-89). Read the article and design some magic square art pieces.

Individual Research Project 1.4

An alphamagic square, invented by Lee Sallows, is a magic square so that not do when the numbers spelled out in words form a magic square, but the numbers of letters of the words also form a magic square. For example,

gives rise to two magic squares:

The first magic square comes from the numbers represented by the words in the alphamagic square, and the second magic square comes from the numbers of letters in the words of the alphamagic square. Find another alphamagic square.

References

William H. Benson and Oswald Jacoby, New Recreations with Magic Squares (New York: Dover Publications, 1976).

John Fults, Magic Squares (La Salle, IL: Open Court, 1974).

Martin Gardner, "The Magic of 3 by 3; The $100 question: Can you Make a Magic Square of Squares?" Quantum, January/February, 1996, pp. 24-26.

Martin Gardner, "Mathematical Games Department," Scientific American, January 1976, pp. 118-122.

http://mathworld.wolfram.com/MagicSquare.html
http://forum.swarthmore.edu/alejandre/magic.square/loshu.html