This
day, 14th March 2015, is something of a special, that can come only
once in a century. If we write today's date in

*(mm/dd/yy)*format, the number will correspond to an mathematical entity that has been puzzling the mankind for more than a millennium. Today's date, 3-14-15 exactly matches with the the first five digits of the number Pi. And if we include a specific time, 9.26 Hrs. 53 Sec, the number thus formed would match the first ten digits of Pi or 3.1415.
What
is a Pi? It is a mathematical constant and an irrational number,
which means it is an infinite decimal and the number never ends.
Simplest definition of Pi is that it is defined as ratio of the
circumference of a circle to its diameter, pi is all around us. The
number is the same for all circles of any size. While we may
remember it's value as 3.14 or 22/7 from our geometry homework,
computer programmes have calculated its value up to trillions of
decimal places.

Who
invented Pi in the first place? According to Wikipedia, the earliest
written approximations of Pi are found in Egypt and Babylon, both
within 1 percent of the true value. In Babylon, a clay tablet dated
1900–1600 BCE has a geometrical statement that, by implication,
treats Pi as 25/8 = 3.1250. In Egypt, the Rhind Papyrus, dated around
1650 BCE, but copied from a document dated to 1850 BC Ehas a formula
for the area of a circle that treats Pi as (16/9)2 ≈ 3.1605. In
India, the earliest Sanskrit text known as Baudhāyana Śulbasûtra
from about 600 BCE gives a value of pi to some degree of precision as
(9785/5568)2 ≈ 3.088. In 150 BCE, or perhaps earlier,
Indian sources treat Pi as ≈ 3.1622.

Archimedes
provided the first theoretical calculation of Pi around 200 BCE. He
said the constant takes the value between 223/71 and 22/7. The
interesting thing is that he did not claim to know the exact value of
Pi, rather he mentioned about the boundary of values between which Pi
exists. He used pure geometry, using the circle and regular polygons
in deriving his expressions in term of fractions.

Indian
mathematician “Aryabhata” made an approximation of Pi, using a
regular polygon of 384 sides and he gave the velue of Pi as
62832/2000, which is equal to 3.1416 and was correct to four decimal
places.

In the
year 1400 CE, another Indian mathematical genius, Madhava from Cochi
in south India used a series for the first time to calculate Pi. His
series was Pi/4 = 1-1/3+ 1/5- ….... and from this series he
calculated the value of Pi as 3.14159265359, which was correct to 11
decimal places.

The
Indian mathematical prodigy Ramanujan discovered a new infinite
series formula in 1910. However its importance was re-discovered
around late 1970's long after his death. With each addition of a term
in Ramanujan's series, it is possible to obtain 8 additional digits
to value of Pi. During 1985, the value of Pi up to 17 million digits
was accurately computed using Ramanujan's series.

Some
more interesting stuff about Pi: only 40 digits of pi are needed to
accurately calculate the spherical volume of the universe. The
Guinness world record for memorising the digits of pi is held by Chao
Lu of China, who recited the number to more than 67,000 decimal
places. The US Congress endorsed Pi Day as a day to celebrate math
education in 2009. Many institutions mark it as a way to encourage
interest in math and science.

Many
people around the world hold events in conjunction with Pi Day. Some
involve eating pies, others the memorising of the digits of pi, and
other educational activities that 'pi-ticipants' can enjoy. I feel
that it may be more appropriate to remember on this day, geniuses of
Aryabhat, madhava and Ramanujan, who gave us the value of this
mathematical constant that has been part of hundreds of mathematical
formulae and series invented over the centuries.

14th
March 2015

Very Interesting and useful informative post. Thanks.

ReplyDeleteMangesh Nabar