2. Pi is ancient
“The fact that the ratio of the circumference to
the diameter of a circle is constant has been
known for so long that it is quite untraceable”
(O’Connor).
The Bible contains a verse that tells us a value
of pi that was used.
“And he made a molten sea, ten cubits from the one
brim to the other: it was round all about, and its height
was five cubits: and a line of thirty cubits did compass
it about”- (I Kings 7, 23)
Here the value of pi is given as 3, not very accurate, not even
for its time.
3. Even the Egyptian and
Mesopotamian values of
25/8= 3.125 and √10=
3.162 have been traced to
much earlier dates than the
biblical value of 3
The earliest values of pi
were almost certainly
empirically determined,
which means they were
found by measurement.
Rhind Papyrus
4. Pi becomes theoretical
It appears to have been Archimedes who was
the first to obtain a theoretical calculation of pi.
He concluded the following: 223/71<pi<22/7
Archimedes used inequalities very
sophisticatedly here to show that he knew pi did
not equal 22/7. He never claimed to have found
the exact value.
It has become one of the most prominent
missions of the scientific community to calculate
pi more and more precisely
6. Pi becomes more and more exact
Ptolemy calculated pi to be 3.1416
Zu Chongzhi obtained the value pi= 355/113
Al-Khwarizmi without knowledge of Ptolemy’s
work found pi to be 3.1416
Al-Kashi calculated pi to 14 decimal places
Roomen calculated pi to 17 decimal places
Van Ceulen calculated pi to 35 decimal places
7. Al-Khwarizmi
Lived in Baghdad
Gave his name to the
word “algorithm”
The word “algebra”
comes from al jabr,
the title of one of his
books
Was the pioneer of
the calculation of pi in
the East
Al-Khwarizmi
8. The art of calculating Pi evolves
Complex formulas are developed in the
European Renaissance to calculate pi.
With these formulas available, the difficulty
in calculating pi comes only in the sheer
time consumption and boredom of
continuing the calculation.
This task is much like Napier’s when he
decided to determine the value for
logarithms.
9. Some people were “dedicated” enough to
actually spend incredible amounts of time
and effort continuing the calculation of pi.
1699: Sharp gets 71 correct digits
1701: Machin gets 100 digits
1719: de Lagny gets 112 correct digits
1789: Vega gets 126 places
1794: Vega gets 136 places
1841: Rutherford gets 152 digits
1853: Rutherford gets 440 digits
1873: Shanks calculates 707 places of which
527 were correct
11. Augustus de Morgan
English mathematician
born in India
Looked at Shanks’ 707-
digit calculation of pi.
Noticed that there was a
suspicious shortage of
7s.
In 1945 Ferguson
discovers that Shanks
had made a mistake in
the 528th place, which
lead to all the following
digits to be wrong.
De Morgan
12. More precision becomes available
Pi was calculated to 2000 places with the
use of a computer in 1949.
In this calculation, and all calculations
following it, the number of 7s does not
differ significantly from its expectation.
The record number of decimal places for
pi calculated in 1999 was
206,158,430,000. However, this record
has already been broken.
13. The Notation of pi
The first to use the
symbol π with its
current meaning was
William Jones in
1706. He was a William Jones
Welsh mathematician.
Euler adopted the
symbol in 1737 and it
soon became a
standard.
Leonhard Euler
14. What does all this have to do with
us?
Throughout the semester we have been
learning about how improvements have
been made in the art of measurement.
Tyco Brahe used instruments the size of
buildings to take accurate measurements
of the movement of the stars and planets.
The constant attempt to improve on our
understanding of pi is similarly to be able
to make more accurate measurements.
15. Just as scientists have tried to calculate
the speed of light to the most accurate
decimal possible, scientists are trying to
define pi to the most accurate decimal. It
is becoming increasingly often that pi is
defined in terms of more decimal places
17. If you want to get a sense of how huge the
amount of decimal places calculated for pi
is, go to the following url (Load time is
pretty long):
http://3.1415926535897932384626433832795
18. Source Used
O’Connor, J. J. and E. F. Robertson. “A History of Pi.” Aug.
2001. University of St. Andrews. 27 Apr. 2004
<http://www-history.mcs.st-
andrews.ac.uk/HistTopics/Pi_through_the_ages.html>.
