# Where did pi come from?

1. Apr 15, 2004

### decibel

what does pi mean, and where did it come from, i know its 3.141592654, but i also know theres alot more decimal places then that, does anyone know anything about it?

2. Apr 15, 2004

### The_Professional

Funny coincidence.I just finished watching that movie a couple of nights ago. I believe the number goes to infinity after the decimal point.

3. Apr 15, 2004

### chroot

Staff Emeritus
4. Apr 15, 2004

### mathman

When I was in 7th grade, I learnt that pi was the ratio of the circumference to the diameter of a circle. I still think it means that today.

5. Apr 15, 2004

### ahrkron

Staff Emeritus
I know you mean no harm, but just be careful how you phrase it. It is true that there is an infinity of digits after the decimal point, but, in math, "goes to infinity" usually means that the quantity itself grows without bound, while pi is no larger than 3.2.

6. Apr 15, 2004

### The_Professional

Thanks for clearing that out :)

7. Apr 16, 2004

### verty

My question is this: is PI defined as the ratio of circumference to diameter, or as the area of a circle of radius 1?

It seems easier to define it as the area of a unit circle, as we can then approximate to the value of PI.

8. Apr 16, 2004

### NateTG

Since the two are the same, it doesn't really matter. In practice, the ratio of diameter to circumference is much easier to deal with than the ratio of square of radius to area.

9. Apr 16, 2004

### mathman

Historically, I believe the circumference to diameter ratio was the definition. Archimedes is reputed to have approximated pi by approximating the circumference by many sided polygons.

10. Apr 16, 2004

### arildno

Actually, Archimedes proved the important result that the constant of proportionality between the diameter and the circumference and the constant of proportionality between the squared radius and the circle's area was the same proportionality constant (pi).
(He showed that the area of the circle had to be equal the area of the right angled triangle with base equal to circumference and height equal to radius.)

He then proceeded as mathman says.

11. Apr 20, 2004

### HallsofIvy

Staff Emeritus
I wouldn't use the word "reputed"! Archimedes definitely did approximate pi by using polygons with up to 96 sides. He did not (as I foolishly thought until recently) actually draw huge polygons and measure the sides! He developed an algorithm for calculating the length of a side of a polygon of 2n sides in terms of the length of side of a polygon of n sides inscribed in the same circle (96= 6*24 and the side of a hexagon is the same as the radius of the circle). He also developed an algorithm for finding upper and lower bounds on square roots since his other algorithm involved square roots. He showed that pi is between 223/71 and 22/7.