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Greek discovery of pi
Name: doug buckwald
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Question:
My students would like to know how the Greeks first calculated
an accurate numerical value for pi. Thanks!
Replies:
They probably sent an e-mail to Cairo and asked an Egyptian. All of
your questions are answered in a nifty little book called "A History of Pi"
by Petr Beckmann (St. Martin's Press 1971-it may have been reprinted by
Dover).
jlu
That's a great book, if you can find it. Most books on the history of
mathematics discuss early measurements of pi along with the beginnings
of geometry.
The ancient Greeks may have gotten some of their math from Babylon but
probably not from Egypt: "...the Egyptians' efforts toward geometry are
mostly trivial and disappointing." (ref. 1, p. 43) and "So far as is
known, nobody before the ancient Greek mathematicians ever "took pi
equal to" anything." (ref. 1, p. 46)
As for how they did it, I imagine they used a piece of twine to draw a
circle of constant radius about some point, then more twine to measure
the circumference of that circle. When they checked a few circles with
differing radii, they would have discovered that the ratio of
circumference to radius was constant.
references: 1. The Development of Mathematics, E. T. Bell, McGraw-Hill, 1945
hawley
I think that later research gives a more favorable view of Egyptian
math. I found Richard J. Gillings, "Mathematics in the Time of the
Pharaohs" quite fascinating. The Egyptian value for pi was 256/81,
which isn't all that bad.
jlu
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Update: June 2012
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