Can any body show me how the value of Pi came to be 3.14 .. ? While, I found out it to be (2 root of 2) ???

Question

Please show me in detail! I'm really excited about this value ???

I just used a simple logic from Calculus!

First, I took a circle with radius as "a". Then, I made the center of the circle as the orgin i.e. I made x and y axes. After that, I took two points at the circumference on each axes (On the first quadrant, though), so Now my point on x axis will be (a,o) and on y axis will be (o,a) right!!! Now, after this, I used ARC LENGTH formula and found out that the length of arc between these two points to be (a * root of 2). So, since this is the arc lenth of quarter of a circle, so the full arc length of a circle or the circumference must be (4 * a * root of 2). So, as circumference of a circle as formulated is given by (2 * Pi * a)- in this case, "r" being "a", I equated two these variables, and found out that the value of PI to be (2 root of 2). So, my question is, how can the value of Pi be more than one, if it is constant ? Shoudn't the value be the same even it is to be calculated by any processes ??? ...

I am not being smarter, please guys!!! I 'm just excited about this!!! So, HELP ME PLEASE!!!

I have already found out that this value was once determined by one of the mathematician, probably like, 3 centuries ago. But, he found out as (2 divided by (1 divided by root of 2) !!! So, same as his, I found out 2 root of 2 instead... So, as the progress went on, the value was, perhaps, found out as 3.14 ... ( with more than 5 million decimal places) !! So, I just want to know the calculation process as simple as you guys can provide. I don't need any lenghthy descriptions cuz it must have been found out through a theory (not theories) with some calculus analysis!!!

I just want to know the process!!!!!!

The formula that i used for arc length is:

arc length = integral from 0 to a [(Sqrt (1+(dy/dx)^2)) dx] --- Here, a being the radius!!

Answer 1

I'd like to know how you found it to be 2*sqrt(2). Pi has been proven to be transcendental, meaning it cannot be a solution to a polynomial equation with rational coefficients. This also means that it is not a square root/cube root/nth root value. There are many interesting approximations for pi which all converge on the same value. Look in the source list for more info.

The "arc length" formula you used had nothing to do with calculus. It looks to me like you used the pythagorean theorem. Regardless of how you got there, this would be the side of a right triangle with 2 legs with length of a. Since a right triangle is not congruent with 1/4th of a circle, your formula is wrong. The length of your arc needs to be longer, since 2sqrt(2) would be the shortest distance between the two points (a line) and the circumfrence of a circle is not a line.

If you really want to use calculus to find the value of pi, try integrating sqrt(1-x^2) with respect to x from 0 to 1, then multiplying by four. That will give you pi. You'll have to do it either numerically or by creating an infinite series, though.

Answer 2

I figured it on a computer in Basic class when I was a wee bairn by calculating what percentage of several billion points in a square were within a circle in the square the same diameter as the side of the square. I also used the same program to prove that the random number generator in the computer wasn't random by seeing if I got closer to Pi with random numbers or fixed regular coordinates.

Answer 3

It is a natural thing. It is the number which relates the ratio of the distance across a circle to the distance around the circle. The fact that this natural number happens to be almost mystical is simply one of naure's mysteries.

There is also a formula which allows you to calculate it with a powerful computer.

Answer 4

The arc length is wrong. What formula were you using?

arc length = radius x central angle (in radians)
= a (pi/2)

Answer 5

You will find history(evaluation) value of pi computaion etc about pi in the link

Answer 6

The value of Pi has been worked on since Ancient Greece and even before that. info has a great article on it,,let me grab that,,,,,
http://www.infoplease.com/ce6/sci/A0838910.html
theres aloltta links at that one.
http://www.highbeam.com/doc/1G1-4702871.html
Them guys are KURaZy!
have fun

Answer 7

the value of Pi=22/7
when u will divide 22 by 7 you will find the answer 3.14.......

Answer 8

it came by 22/7 equals 3.142

Answer 9

check out these sites:

http://mathforum.org/dr.math/faq/faq.pi.html

http://en.wikipedia.org/wiki/Pi

http://www.cecm.sfu.ca/~jborwein/pi_cover.html