What are two ways that Pi can be calculated?

Question

What are two methods that can be used to find the value of Pi? I then need to prove that they work by substituting values into the method (or equation). Thanks!

Answer 1

There are several ways which use the fact that arctan(x) can be approximately calculated for any value of x by summing sufficient terms of its Maclaurin series:
x - x^3/3 + x^5/5 - x^7/7 + ...

The formula Pi = 4 x arctan(1) is correct but very slow to converge.

Pi/4 = 4 x arctan(1/5) - arctan(1/239) is called "Machin's formula" and historically has been used for the longest time.

More formulas for Pi are described and discussed at the web page below, but the mathematics is quite heavy.

Answer 2

One way PI can be approximated is by the infinite series:

4(1 - 1/3 + 1/5 - 1/7 + 1/9 - .... )

The more terms you add, the more accurate it gets.

Answer 3

Just use the two equations for pi-:

Area = pi x radius x radius

Therefore-:
(area / (radius x radius)) = pi

Circumference = 2 x pi x radius

Therefore-:

pi = (Circumference / (2 x radius))

Best of luck with your calculations

Answer 4

1.draw a circle, and measure its perimeter, then divide by its diameter, this is old method to find Pi value.
2.I don't know :)

Answer 5

Pi is the ratio of the circumference of a circle to its diameter

Pi = circumference / diameter

- - - - - - - - -s-

Answer 6

Pi=Area/Radius^2
\pi = \frac{1}{2^6} \sum_{n=0}^{\infty} \frac{{(-1)}^n}{2^{10n}} \left( - \frac{2^5}{4n+1} - \frac{1}{4n+3} + \frac{2^8}{10n+1} - \frac{2^6}{10n+3} - \frac{2^2}{10n+5} - \frac{2^2}{10n+7} + \frac{1}{10n+9} \right)

Answer 7

Pi = 22/7 = 3.142
By applying logarithms log 22 - log 7 = 1.3424 - .8451
= .4973
Anti log of .4973 = 3.143

Answer 8

One way is 22/7