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I think it also helps to understand why the diameter of the circle is proportional to the circumference if you do a drawing. Draw a square; it helps if you use graph paper. Now use a compass to draw a circle inside, so that the circle touches the inside of the square in the four places where the diameters of the circle are also cutting the square in half, both in length and width. I find that sometimes this picture helps people to see that the circumference of the circle is related in a specific way to its diameters, and to the square containing the same length sides.
Pi (from the greek word that means 'periphery') is simply a ratio, or a fraction of the circumference (distance around a circle) to its diameter (distance across a circle) or
1) circumference / diameter, or c/d
One of the properties of all circles, no matter how large or small, is that the fraction of circumference and diameter will always reduce to 22/7, so if the distance around a circle is measured as 22, the diameter of that same circle is always 7. If the diameter is 14, the circumference is always 44, and so on. However, since 22/7 is simply a fraction, although a very special one, it can be represented in decimal form
2) 22/7 = 3.1416....
Since 22 divided by 7 doesn't come out evenly, the number goes on forever, but rounding it to 4 digits is usually good enough for calculations. So this 22/7 fraction, or this 3.1416 decimal number, is given the special name of Pi.
It is almost sure that first values of pi number were found by measuring. The first person who gave us a value of pi number was the Egyptian named Rhind Papyrus, in the year 1650 before Christ. He found that pi number has the value 3,16.
Though, the first theoretical calculation of pi number was made by Arhimede of Syracuse (287 - 212 B.C.). He found the inequality: 223/7 < pi < 22/7. Introducing this inequality, Arhimede proved that he knew something what others doesn't know nowadays (pi has not the value 22/7). Arhimede has not made the statement that he found the value of pi number. If we use the most accurate of estimations, we could obtain the value 3.1418.
Anyway, we must know the fact that the ratio of the each and every circle circumference and it's diameter is non-variable, and always has the same value, 3,1416.
Nowadays, the number pi is known with the precision which is about 64 billions of decimals.
It is a mathematical constant, and the ratio of this pi is between the circumference of the circle and its corresponding diameter. Like this, if circumference is 44cm, then diameter would be 44/22*7= 14cm. It is also the same value as the ratio of the area of the circle to the square of the radius. Pi can be expressed as 22/7 or 3.142.
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