The value of π has engaged the attention of many mathematicians and calculators from the time of Archimedes to the present day, and has been computed from so many different formulae, that a complete account of its calculation would almost amount to a history of mathematics. - James Glaisher
π is the ratio of the circumference to the diameter of a circle. π has been calculated by different people throughout history.
The earliest calculations of π appear in the Bible as approximately 3 and in the Egyptian Rhind Papyrus as approximately 3.16 (O'Connor).
The Bible calculated π to be 3 when it stated,
And he made a molten sea, ten cubits from 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.
-1 Kings 7:23. Here you can learn more and see the calculations (Stapel).
An ancient civilization used 3 to approximate the circumference of a circle (PI). The Babylonians were able to calculate π to be 3.125 (Pi | mathematics).
In the Rhind Papyrus, the Egyptians calculated a formula for the area of a circle.
This calculation gave π the approximate value of 3.1605.
The Babylonians also calculated the formula for the area of a circle as 3 times the square of the radius.
This gave π the approximate value of 3 (Pi Day: History of Pi).
Euclid was able to prove the existence of π (Barnes).
Then the Greeks were able to get a closer approximation, and Archimedes is credited with the first theoretical approximation of π.
Then in 1761 Johann Lambert proved that π was an irrational number (PI). In 1882 Ferdinand von Lindemann proved that π was a transcendental number (PI).
Now with computers π can be calculated to the first six billion digits (Bogart).
The oldest calculations can be traced to the Bible and the Rhind Papyrus. The Rhind Papyrus which is from ancient Egypt has π calculated to be 3.1605.
π wasn,t named until three thousand years after the Rhind Papyrus and was just referred to as the quantity which, when the diameter is multiplied by it, yields the circumference (Blatner).
The Bible calculates π to be three, but late-eighteenth century Rabbi Elijah of Vilna discovered that the Bible also calculates π to be 3.1416.
He discovered that in 1 Kings 7:23 the Hebrew word for line of measure is written differently than it is in 2 Chronicles 4:2.
When he interpreted line of measure from each of the two passages using a technique called gematria, he got 111 and 106.
He then took the ratio of 111/106 and multiplied it by the Bible's calculation of three he got 3.1416, which is π correct to four decimal places (Posamentier).
The Greeks were interested in a precise calculation of π. The Greeks were interested in precise mathematical definitions to describe the world around them.
There were close approximations for π, but Archimedes came up with a theoretical approximation for π as opposed to the measured calculations that were around before him (Groleau).
Archimedes was able to calculate π by approximating the area of a circle with radius one by calculating the area of a polygon inscribed in the circle and then calculating the area of the polygon the circle was inscribed in.
Then he knew the area of π had to be somewhere in between the two polygons (Pi Day: History of Pi). Click here for an applet on calculating Achimedes' Method. Archimedes began with a hexagon for his polygons and went all the way to a 96-agon (a polygon with 96 sides) (The Amazing History of Pi).
He was able to calculate that π was in between 3 1/7 and 3 10/71 (Pi Day: History of Pi).
π has been calculated in many different ways, but one of the most interesting ways was done by French mathematician Georges Buffon. Buffon calculated π by using probability.
Buffon took a uniform grid of squares and dropped needles on the grid; he then calculated the probability that the needle will fall on a line in the grid (The Amazing History of Pi). Buffon's Needle Problem
Buffon's needle problem is a problem in geometric probability.
The answer to this problem is the case where the length of the needle isn't larger than the width of the strips.
The solution can then be used to design a Monte Carlo Method for approximating π.
So even though that is not what Buffon originally set out to do, it works as an approximation for approximating π (Buffon's needle).
Buffon's Needle Problem
If you wanted to do Buffon's needle problem on your own, you could!
All that you will need is a needle, toothpick, pencil, pen, or even a hotdog!
It just needs to be long and skinny. After you have whatever object that you want to use as your needle, measure the length of it and call that length one unit.
Then take a piece of paper and draw several parallel lines that are one unit apart from one another.
Then drop your needle onto the paper at least twenty times, the more you drop it the better!
When you're dropping it, count how many times you drop it and how many times the needle is touching one of the lines on the paper after it has landed.
After you collect all this data multiply how many times you have dropped your needle by two.
Then divide this by the number of times it touched one of the lines. Did you get π?
The probability of the needle hitting the line is 2/π. So then 2/π=(number of times it hits the line)/(number of times dropped).
We can rearrange this equation and get π=(2(number of times dropped))/(number of times it hits the line).
For the full proof and a simulation click here (Jenkins).
Also, here is a video simulation of Buffon's Needle Problem.