Born ????                             Died 1741

Muhammad ibn Muhammad al-Fullani al-Kishnawi lived in Katsina (now Nigeria), but spent most of his mathematical career in the Middle East.  Muhammad traveled to Egypt and wrote a manuscript (in Arabic) of procedures for constructing magic squares up to order eleven.

Muhammad was a man of many talents.  He was an astronomer, mathematician, mystic, and astrologer.  He was also a member of the Fulani people, a group of Africans that are extremely devoted to Islam.  The Fulani people were one of the first people converted to Islam.

Muhammad is noted for saying “work in secret” and for saying “Do not give up, for that is ignorance and not according to the rules of this art.  Those who know the arts of war and killing cannot imagine the agony and pain of a practitioner of this honorable science.  Like the lover, you cannot hope to achieve success without infinite perseverance.”

Muhammad’s math was to come up with an easier way of developing magic squares.  A magic square is a square in which the numbers in the columns, rows, and main diagonals add up to the same constant.  This constant is known as the magical constant.  For instance, if you look at the magic square on the next page and add the numbers in the first row, four plus nine plus two, you will find they equal the sum fifteen.  Likewise, the column four plus three plus eight also equals fifteen.  Sum up both diagonals and you will see they equal fifteen as well.  Fifteen is the magical constant.  Muhammad came up with two formulas; one to find out the middle number in the square and the other was to find the magic constant.  These two formulas are (n(n^2 + 1))/2 for the magic constant and (n^2 + 1)/2 for the middle number.  The middle number in this same square is five.  The variable N in both of these formulas is the order of the magic square, which is found by counting the number of rows or columns.  For example, the order of the magic square on the next page is three.

Even though Muhammad was not considered a minority in his native land, because of his career he was.  Also in the mathematical world Muhammad was considered a minority because he was not Anglo-Saxon or Christian.  In this time, black people were supposedly not capable of conquering mathematics.  Despite these challenges Muhammad persevered and never gave up.

# TRUE OR FALSE

1.              Muhammad worked with others on his math.

2.              Muhammad said if you do not understand give up.

3.              Muhammad was a follower of the religion Islam.

4.              Muhammad came up with magic squares.

5.              We know the year in which Muhammad was born.

If you have a magic square you can create others by rotating the numbers about an axis.  As long as the numbers are still in the same column and row, it is the same square.

 4 9 2 3 5 7 8 1 6

For example take the magic square above.  The magic square below is the same square only rotated about a one hundred and eighty degrees about the y-axis.

 2 9 4 7 5 3 6 1 8

Now using the formulas on the first page tell what the middle number and magic constant is for a magic square of order seven.

Fill in the squares.

 3 4 1 5 6

 3 7 11 8 25 12 9 21 13 5 17 14 1 18 15 19 23

References:

Africa Counts:  Number and Pattern in African Culture

Claudia Zaslavsky