might seem surprising to a modern:
An equivalence is demonstrated by stretching the circle's perimeter to
a straight line (like removing the belt on a garment). The triangle with
the circle's radius is the area of the circle!
http://accromath.uqam.ca/2013/04/regard-archimedien-sur-le-cercle-quand-la-
circonference-prend-une-bouffee-daire/
Pythagoras Samos 570-495 BC
Zeno Elis 490-430 BC
Archimedes Syracuse 287-212 BC
Archimedes was the first to try to measure pi with precision, with
was is called the method of exhaustion. By that time, Eudoxus of Cnides
-in Turkey - (390-337 BC) had found that 2^.5 was irrational.
A's method consisted of adding polygons both inside and outside the
circle. At 90 sides, he estimated pi to be:
3.1408 < pi < 3.1429. In 150 AD, Ptolemy made it to 3.1416. By 1630,
Europeans were at 39 digits.
François Viète 1540-1603 was the first to use letters to replace quatities.
He created the first series - a multiplications one - to approximate pi.
It is still useful today.
To use Viète's series, see the calculator below. At 100 iterations, all the 25
decimals shown are valid. In fact, they are valid before that... Have fun!
source: Wikipedia
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