Question

pi is defined as the ratio of the circumference to the diameter of a circle, and it is an irrational number, right? It's value is evaluated to be 3.14...... and so on, and computers are still evaluating. My question is which circle's ratio of circumference to the diameter is being solved to obtain the value for pi? And what are those values of circumference and circle, which evaluates the value of pi?

Answer 1

All circles!

Answer 2

"Circumference of the circle" to the "diameter of the circle"

Answer 3

@Mr. Math: All circles, right, so what are those values of circumference and diameter, which evaluates the value of pi?

Answer 4

I mean, what number, do you divide with what number? as to get the answer 3.14......

Answer 5

The ratio of the circumference of any circle to its diameter is pi.

Answer 6

you can read a little bit about how \(\pi\) was discovered here: http://www.gap-system.org/~history/HistTopics/Pi_through_the_ages.html

Answer 7

You divide \(2\pi r\) by \(2r\) (i.e there's no restriction on the diameter or the circumference).

Answer 8

Mr.Math is right - as usual :-P
Just for the record, pi is irrational. You'll never get 3.14 exactly (unless by some coincidence sufficient rounding error lands you with this solution - but don't expect it!).

Answer 9

So you got it, right? Circumference to diameter is\[\pi=\frac{C}{d}\]the circumfrance C is\[C=2\pi r\]and the diameter is\[d=2r\]so the ratio is\[\frac{C}{d}=\frac{2\pi r}{2r}=\pi\]The radius r cancels every time, regardless of the size of the circle...

Answer 10

\[\tau= 2pi r\]

Answer 11

\[\tau r=2\pi r\]

Answer 12

I actually understand this, what I don't understand, is how computers and the scientists, achieved to find the value of pi, they how did they calculated?

Answer 13

That is a much better question

Answer 14

Read the article asnaseer linked, and otherwise search for "pi." I once saw a documentary on the subject - very fascinating - but I'm afraid I can't remember now.

Answer 15

How do the computers evaluate the value? Some numbers have to be divided by some number to get the decimal places after 3.14? or even 3.14? What are they?

Answer 16

I don't know exactly what king of programs are used, but I know there have been a variety of them, making use of thing like the way you can divide up a circle into triangles.

Here are a list of many (doubtfully all) methods used to calculate pi:

http://www.gap-system.org/~history/HistTopics/Pi_chronology.html

but asnaseer's link is better for detail.

Answer 17

Another article on how to calculate \(\pi\): http://www.faqs.org/faqs/sci-math-faq/specialnumbers/computePi/

Answer 18

...so in that link it says a computer used the "based on the Gauss-Legendre algorithm and Gauss arctangent relation" which I do not know the meaning of.

But other methods used before may be more accessible.

Answer 19

i advise u not to go in such depth as it will screw u

Answer 20

@wasiqss - there is no harm in someone trying to find out more about the background of a particular subject or topic - it strengthens your knowledge by reinforcing your foundation.

Answer 21

lolz anaseer u lack xperience :P, i use to take keen interest bt i always ended up screwing, n the concepts i had also got vanished :P s

Answer 22

well - lets just say I will agree to disagree with you @wasiqss

Answer 23

well do wut u want who carex :P

Answer 24

@wasiqss - you need to have a more positive attitude towards things - it will help you calm down and understand things better :-)

Answer 25

Thank you everyone for the help. It really helps. :)

Answer 26

yw

Answer 27

anaseer jus tel me wut grade u in?

Answer 28

n sorry if u did mind

Answer 29

@wasiqss - I'm currently working as a software engineer but I keep in touch with maths by /trying/ to teach others.

Answer 30

n im doin electronics engineerin :P

Answer 31

which year are you in?

Answer 32

1st

Answer 33

great! - I hope you enjoy your course