Welcome to the world of mathematics. Believe it or not, you have been living in a world synchronized by numbers for your entire life. Everything has a shape, and in order to get to that shape, numbers are needed. You might say that anything round is "pied" because in order to get the area of it, you need that special ratio. If pi were just 3, then we wouldn't have circles in three-dimensional space as we know them. In a black hole, a point in space so dense that even light deflects towards it and cannot escape, the ratio of circumference to diameter is closer to 4. We might have something like Edwin Abbott's Flatland if pi were less than its current value.
A Brief History
The first famous "pi people" in history were probably the very first people on the planet. They saw circles everywhere: in other people's eyes, the Moon, the Sun, etc. In order for these people to make the first step in determining pi, however, they had to understand the concept of magnitude. For example, the bigger a stone is, the heavier it is. The smaller the stone, the lighter it is. From these simple observations, prohuman then had to realize that some things have direct proportional relationships. He had to look at a circle and think, "The wider a circle is 'across', the longer it is 'around.'" From this, a very profound statement would be, "No matter how long or wide a circle is, the relationship between them is always the same."
The first cultures given credit for finding a value of pi are the Babylonians and the Egyptians. In the year 2000 B.C.E., the Babylonians determined that pi is equal to 3 1/8 and the Egyptians arrived at 4(8/9). Both got these values, probably, by drawing a circle in the sand and measuring the distance around it with a rope. That point on the rope is then marked and then the distance across it is measured. To determine pi, the person would have to see that the circumference is about three times the length of the diameter, with a little bit left over. Obviously, it's impossible to tell just by looking that the little bit is really approximately .1415926535897932384626433832795028841971693993751058209749445923078164062862099, so the 1/8 (.125) that the Babylonians came up with is not very far off for that time period.
Another early record (1650 B.C.E.) of pi is located on the Rhind Papyrus, written by a scribe by the name of Ahmes. On the papyrus are 84 math problems and their solutions, though it doesnít say exactly how the solutions were found. Ahmes writes that the area of a circle with a diameter of 9 is the same as a squareís area with a side of 8 units. With the formula A=
r^2, the Egyptian value of pi becomes =4 x 8/92, which is 3.16049. Other problems on the papyrus show the first attempts to build a square with the same area as a circle.
In the 3rd century B.C.E., Archimedes of Syracuse tried another method of squaring the circle. He drew a circle and inside the circle he draws a hexagon. From the hexagon, he constructed more and more sides on to it until arriving at a a polygon with as many sides as he could fit. With a 96 sided polygon, he figured out that pi is greater than 3.140 but less than 3.142. He arrived at those values without trigonometry (let alone a calculator). Astounding!
The next major "digit hunter" of our story is Leonardo de Pisa in 1220, otherwise known as Fibonacci. He is well known for the Fibonacci sequence
Why Pi?
to mean what it means today! That's right! Even though pi itself is a Greek letter, the Greeks thought of it as just that. Pi has only been widely recognized as the symbol for the ratio of circumference to diameter for the past 250 years. 17th century mathematician William Oughtred was probably the first to use pi to mean any number. In 1652, he used pi to stand for circumference in a constant proportion to its diameter, but never used one symbol for that ratio. In 1689, a Bavarian professor J. Christoph Strum used the letter e to represent what we know as pi. For another hundred years, most other mathematicians were still using notations such as c/d.
This book was not nearly as influencial as Leonhard Euler's (OIL-er's) work, which made
How Can I Calculate Pi?
And, duh, of course I know there's aMETHOD 1: 4[5arctan(1/7) + 2 arctan(3/79)]Both of these are based on the fact that the tangent of
METHOD 2: 4[2 arctan(1/3) + arctan (1/7)]
You too can create an infinite series for pi, even if you don't know or remember anything from Calc I! Just click these underlined words!
Without proof, here are a few more series, courtesy of some of the greatest mathematicians of all time:
Euler's infinite series:
Newton's infinite series:What is Pi? | Fun With PI | Calculate Pi | Pi Poetry | Fan Fiction | Links | Message Boards | Webrings | Mathemagic
