HISTORY OF MATHEMATICS – LECTURE 6 – TUESDAY 13
TH
SEPTEMBER
Pi
Approximating the value of the ratio of a circle’s circumference to its diameter has interested
mathematicians for thousands of years. Even the Old Testament contains an implicit approximation in
1 Kings 7:23 (written around 650 B.C.):
“And he (Solomon) made a molten sea, ten cubits from the one brim to the other: it was round all
about, and his height was five cubits: and a line of thirty cubits did compass it round about.”
The approximation of 3 is a natural starting point; however there is evidence that both the Egyptians
and the Babylonians had better estimates. The Rhind Papyrus contains a problem and solution which
read:
“Example of a round field of a diameter 9 khet. What is its area? Take away 1/9 of the diameter, namely
1; the remainder is 8. Multiply 8 times 8; it makes 64. Therefore it contains 64 setat of land.”
By comparison with the known formula for the area of a circle, A =
d
2
/4, this answer implies an
estimate for pi of 3.16049…, which is accurate within 0.6%.
A Babylonian tablet found in 1936 ascribes constants to various polyhedral, indicating the ratio of the
perimeter of a regular hexagon to the circumference of a circle, which was stated as 24/25. So if we
construct the diagram below:
then we get that
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View Full DocumentArchimedes
While there are many legends concerning Archimedes which likely have little correspondence to the
truth (for example, running through the streets naked shouting “Eureka”), there is no doubt that he was
one of the greatest mathematicians, developing theories that were far ahead of his time, and is
regarded by many as one of the three most important mathematicians in history, along with Newton
and Gauss.
Archimedes was born around 287 B.C. in Siracusa (Syracuse), Sicily. While he was greatly respected
during his lifetime, his work did not have the enduring of Euclid, as it was too advanced for most people
to understand. Indeed it seems that Archimedes was frustrated by the few people with whom he could
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 Spring '08
 EVINSON
 Calculus, Approximation, Archimedes

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