Muhammad ibn Muhammad al-Fullani al-Kishnawi
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.
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 |
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3 |
5 |
7 |
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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.
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2 |
9 |
4 |
|
7 |
5 |
3 |
|
6 |
1 |
8 |
Rotate the same square about
any other axis of your choice.
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|
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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.
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3 |
4 |
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1 |
5 |
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6 |
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3 |
|
7 |
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11 |
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|
8 |
25 |
12 |
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|
9 |
21 |
13 |
5 |
17 |
|
|
14 |
1 |
18 |
|
|
15 |
|
19 |
|
23 |
References:
Africa Counts:
Number and Pattern in African Culture
Claudia Zaslavsky
Muhammad ibn Muhammad al-Fullani al-Kishnawi web page
www.math.buffalo.edu/mad/special/muhammad_ibn_muhammad.html
Historia Mathematica 21 (1994), 345-376
On Mathematics in the History of Sub-Saharan Africa
Paul Gerdes