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 Is
it a children’s game? Is it an obscure orgami design? Is it some sort
of Ancient Greek Rubik’s Cube? For centuries, Archimedes treatise called
the Stomachion, only fragments of which survive, has fascinated, well,
people who are fascinated by ancient Greek mathmatical mysteries.
Now a historian of mathmatics professor at Stanford has combined archeology,
manuscript restoration and mathmatical thoerizing to finally figure
out what the old
guy was after. Turns out the Stomachion was all about inventing "combinatorics",
the next practicioner of which wouldn’t take up the cause for almost 2200
years….
It was chance that led Dr. Netz to his first insight into the nature
of the Stomachion. Last August, he says, just as he was about to start
transcribing one of the manuscript pages, he got a gift in the mail,
a blue cut-glass model of a Stomachion puzzle. It was made by a retired
businessman from California who found Dr. Netz on the Internet as a renowned
Archimedes scholar. Looking at the model, Dr. Netz realized that a diagram
on the page he was transcribing was actually a rearrangement of the pieces
of the Stomachion puzzle. Suddenly, he understood what Archimedes was
getting at.
The diagram involved 14 pieces, and the word "multitude" seemed
to be associated with it. Mr. Heiberg and those who followed him thought
this meant that you could get many figures by rearranging the pieces.
"This is part of the reason people didn’t see what it was about," Dr.
Netz said. But the old interpretation seemed trivial, hardly worth Archimedes’
time. As he examined the manuscript pages, piecing together their text,
he realized that what Archimedes was really asking seemed to be, "How
many ways can you put the pieces together to make a square?" That
question, Dr. Netz said, "has mathematical meaning."
"People assumed there wasn’t any combinatorics in antiquity," he
went on. "So it didn’t trigger the observation when Archimedes says
there are many arrangements and he will calculate them. But that’s what
Archimedes did; his introductions are always to the point."
from the
New York Times
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