the value of pi is figured out to be 3.14.But question that arises is"HOW?"
2007-01-20 04:36:27 · 9 answers · asked by aman_atal_007 2 in Science & Mathematics ➔ Mathematics
That's a question that lots of scientists and mathematicians have been working on for a long time. My best solution would be to take a perfectly circular object, like a plate or bowl, and first measure it's diameter, and then it's circumference, being as precise as humanly possible. Then divide it's diameter into the circumference.
2007-01-20 05:17:09 · answer #1 · answered by stephieSD 7 · 1⤊ 1⤋
You can find it through the approximation series:
P = 4 (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 + ..... )
The terms in brackets are an infinite series, and you get a better answer the more values you put in.
Contrary to what others might say, you can NOT get the value of pi using 22/7; although 22/7 is coincidentally close to pi, it doesn't serve as a means of getting a closer and closer approximation to pi as the above series.
2007-01-20 12:42:41 · answer #2 · answered by Puggy 7 · 2⤊ 1⤋
The famous series mentioned by Puggy is derived from the following Taylor Series:
arctan(x) = x - x^3 / 3 + x^5 / 5 - x^7 / 7 + ...
For that series, arctan(1) = (pi/4) = 1 - 1/3 + 1/5 - 1/7 + ... Well, that's an interesting formula, but unfortunately, the series convergely too slowly to be very useful. There are other series utilitzing that arctan Taylor series that converge much more quickly. For example, Machin developed a popular one in 1706, which he used to calculate pi to 100 places: (Naturally, since this was in the 1700s, the calculation had to be done without the help of a computer.) Machin's formula is :
pi / 4 = 4 arctan(1/5) - arctan(1/239)
Combine that with the Taylor Series again, and you have a fast converging series - one, in fact, that enables you to calculate pi to several decimal places fairly quickly without a computer.
http://ic.net/~jnbohr/java/Machin.html
2007-01-20 13:20:03 · answer #3 · answered by Anonymous · 0⤊ 0⤋
pi is the ratio between the circumference of a circle to its diameter. This ratio roughly equals 22/7. That is why pi is mostly valued at 3.14.
22/7 = 3.14.............
But this is only a rough value.
2007-01-20 12:51:19 · answer #4 · answered by Riyah 3 · 2⤊ 0⤋
draw a circle of a known diameter
Let us assume the diameter = d
Take a thread. Put it on the circumference of the circle carefully. Measure the length of the thread required to complete the circle accurately.
Divide 'length if the thread' by the 'diameter'. If your measurements are accurate, you will get the value of pi....
2007-01-21 13:35:47 · answer #5 · answered by plato's ghost 5 · 0⤊ 0⤋
You can look it up online and get it to a million digits, but your question is a great one. It is not 22/7 though that is a good approximation.
2007-01-20 12:45:32 · answer #6 · answered by Nelson_DeVon 7 · 3⤊ 0⤋
pi is given by ration of circumference of a circle to the diameter of that circle.
2007-01-21 06:29:45 · answer #7 · answered by Tariq M 3 · 0⤊ 0⤋
Im not sure... but I do know this:
http://en.wikipedia.org/wiki/Pi
-- AND --
http://3.141592653589793238462643383279502884197169399375105820974944592.com/index1.html
2007-01-20 20:46:05 · answer #8 · answered by osufitchi 3 · 0⤊ 0⤋
22/7 is the actual value. this is rounded to 3.14
2007-01-20 12:42:49 · answer #9 · answered by Karunakaran A 1 · 0⤊ 5⤋