Project 1.1

What do the following people have in common?

Ralph Abernathy, civil rights leader
Harry Blackmun, Associate Justice of the U.S. Supreme Court
David Dinkins, Mayor of New York city
Art Garfunkel, folk-rock singer
Alexander Solzhenitsyn, Nobel prize winning novelist
J. P. Morgan, banking, steel, and railroad magnate
Michael Jordan, basketball superstar

Project 1.2

Find some puzzles, tricks, or magic stunts that are based on mathematics. Write a paper describing the tricks and also indicate why they work.

References

William Schaaf, A Bibliography of Recreational Mathematics (Washington, D.C.: National Council of Teachers of Mathematics, 1970).
See also the Journal of Recreational Mathematics. Try this search engine: YAHOO Search Results:
http://search.yahoo.com/bin/search?p=math+puzzles
(over 50 excellent sources)

Project 1.3

A 4-by-4 magic square is shown in this 1514 engraving by Durer called Melancholia. A detail of the magic square is shown:


Notice the date appears in the magic square. Can you see additional properties in addition to the usual magic square properties?
Hint: Add the corners, or the center squares, or the slanting squares (2, 8, 9, 15, for example).

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.

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

Project 1.5

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.

Project 1.6

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.

Project 1.7

Answer the question posed in Problem 59 for your own state. If you live in California, then use Florida.

References

Check an almanac to find the area of your state. Also, most states have a web site which provides this information.

Project 1.8

Read the article, "Mathematics at the Turn of the Millennium," by Phillip A. Griffiths, The American Mathematical Monthly, January, 2000, pp. 1-14. Briefly describe each of these famous problems:

a. Fermat's last theorem
b. Kepler's sphere packing conjecture
c. The four-color problem

Which of these problems are discussed later in this text, and where?
The objective of this article was to communicate something about mathematics to a general audience. Discuss how well did it succeed with you?