m)+Pi

The mathematical constant PI is what you get when you divide the circumference of a circle by the diameter. It’s always the same fixed number regardless of the size of the circle. Fact is, for any circle it’s always three and a bit time’s further round the outside than it is straight across the middle. The figure is quoted to various accuracies, like 3.14, or twenty-two divided by seven, or 3.142,3.14159 or 3.14159265358979323846264338327950288419716939937510….. Euclid proved that this ratio C/D is always the same, no matter the size of a circle.

What is pi? How do you use pi to find the area of a circle? These questions are all about to be answered.

What is pi (the symbol is the small Greek letter )? It is equal to C/d, or C/2r, where C is the circumference of any circle, and d is its diameter, and r is its radius. Euclid proved that this ratio (C/d) is always the same, no matter the size of the circle. What he did was inscribe similar regular polygons in any two circles. Then, he increased the number of sides of the inscribed regular polygons. He reasoned that as the number of sides increased, the perimeter of the inscribed polygon gets closer and closer to the circumference of the circle. He also showed that the perimeters of the similar polygons were proportional to the radii of the circles in which they were inscribed. And so, C is proportional to r, in other words C/r is a constant. By convention, **pi=C/2r**. And we can use that as our definition of pi. area of a circle The area of a circle: at the top of this article, I said that Euclid proved that C/2r is a constant. C/2r eventually became known as pi, and is our definition of pi. We need to figure out the area of a circle. Let's say that we approximate a circle with a regular polygon of n sides. This diagram shows three of those sides, with length P/n (where P is the perimeter of the polygon). And I have drawn a triangle by drawing two of the radii. The area of this triangle is approximately Pr/2n (the altitude is close to r), and as the number of sides of our polygon increases, the area of the triangle gets closer and closer to Cr/2n. In other words, the altitude of the triangle gets closer and closer to r, and the perimeter of the polygon gets closer and closer to the circumference of the circle. There are n of these triangles filling up the circle. So the area of the circle is about A=nCr/2n=Cr/2. Our definition of pi was **C** =2(pi)r= . Substituting this for C, we get =**A**= (pi)r2. So we now know where these two. If you don't understand the formula. a popular way to prove the area formula is to arrange slices of the circle as shown here. As the slices get thinner, the figure gets closer and closer to a rectangle with sides of r and c/2. We can substitute 2(pi)r for c (definition of pi). Then **A=(pi)r2**
 * Definition of pi:**

posted by **privatedancer**.

Is there an easier way to explain pi?

Posted by Craxyjosh:

Pi is 3.14159265358979323846

Or in simpler terms, 3.14. The origin of pi goes back many years, as far as the Ancient Greeks.a man named Archimedes a Greek mathematician/engineer discovered PI. Pi(3.14159265358979323846) which is simply known as 3.14. Archimedes discovered many uses for pi like the area of a circle, circumference and the area of a rectangle.


 * Posted by DummyDerrick**

Actually, I don't think Archimedes discovered pi, it is unknown... Pi was actually known along time ago, around 1900 BC. It was used my many ancient Egyptian, Babylonian, Indian and Greek mathematicians.