Extraordinary Pi
History:
The ancient Babylonians generally calculated the area of a circle by taking 3 times the square of its radius (π=3),
but one Old Babylonian tablet (from ca. 1900-1680 BCE) indicates a value of 3.125 for pi.
Ancient Egyptians calculated the area of a circle by the following formula (where d is the diameter of
the circle):[(8d)/9]2 .This yields an approximate value of 3.1605 for pi.
The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He
obtained the approximation as 223/71
As mentioned above, pi represents the type of numbers called irrational numbers which has endless decimal form
with out any pattern. Calculation of the exact value of pi started very early days of modern mathematics.
The letter Pi
Pi or π is a mathematical constant and a transcendental (and therefore irrational) real number approximately
equal to 3.14159, which is the ratio of a circle’s circumference to its diameter in Euclidean geometry.
An irrational number is a number that cannot be expressed in the form p/q where p and q are integers and q != 0.
In other words, an irrational number is a non terminating non repeating decimal number, with number of decimals extending infinitely.
Pi is also known as Archimedes’ constant and as Ludolph’s number. Pi is the number of times a circle’s diameter will
fit around its circumference. When referring to this constant, the symbol π is always pronounced like “pie” in English,
the conventional English pronunciation of the letter.
The symbol for pi:
The English mathematician William Jones introduced it in 1706, who wrote:
3.14159 = π. This symbol was adopted by Euler in 1737 and became the standard symbol for pi.
Definition:
In Euclidean plane geometry, π is defined as the ratio of a circle’s circumference to its diameter.
π=C/d
Euclid of Alexandria
(325 – 265 BC) is the one who proved that the ratio of C over d is always the same, regardless of the size of the circle.
Alternatively π can be also defined as the ratio of a circle’s area to the area of a square whose side is the radius:
π=A/(r x r)
Numerical value:
The numerical value of π truncated to 50 decimal places is:
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
Uses:
Pi occurs in hundreds of equations in many sciences including those describing the DNA double helix,
a rainbow, ripples spreading from where a raindrop fell into water, superstrings, general relativity,
normal distribution, distribution of primes, geometry problems, waves, navigation.
Interesting:
Pi Day and Pi Approximation Day are two unofficial holidays held to celebrate the mathematical constantπ(Pi).
Pi day is celebrated on March 14 at the Exploratorium in San Francisco (March 14 is 3/14) at 1:59 PST which is 3.14159. And more interestingly the Albert Einstein date of birth is 14th March 1879(3/14/1879).
You will not get zeros in the first 31 digits of Pi. In 1768 Johann Lambert proved Pi is irrational.
It would be interesting to know that there is an International competition to recite the value of pi.
There are people who can recite more than 700,000places! Even there are great records. A Japanese mental health counselor recited the value of pi to 100, 000 decimal places in Tokyo in 2006.
Mathematicians and super computer experts have worked out pi to more than 5 million decimal places using super computers. Research is still going on in this direction.
Additional Links for Pi
Click here for samples
Click here for Mathematics Dictionary
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