Here's a clever way to find $\pi$ (see Cheney, et. al, 5th ed., p. 39). See if you can translate this "pseudo-code"
into a working program to find $\pi$. It'll allow you to practice with for-loops and programming
formulas into the computer.

$a\leftarrow\sqrt{2}$

$b\leftarrow 0$

$x\leftarrow 2+\sqrt{2}$

for k=1 to 5 (or more)

$t\leftarrow \sqrt{a}$

$b\leftarrow t(1+b)/(a+b)$

$a\leftarrow \frac{1}{2}(t+1/t)$

$x\leftarrow xb(1+a)/(1+b)$

output x

end-for

$a\leftarrow\sqrt{2}$

$b\leftarrow 0$

$x\leftarrow 2+\sqrt{2}$

for k=1 to 5 (or more)

$t\leftarrow \sqrt{a}$

$b\leftarrow t(1+b)/(a+b)$

$a\leftarrow \frac{1}{2}(t+1/t)$

$x\leftarrow xb(1+a)/(1+b)$

output x

end-for

Type your code here:

See your results here:

At some point, to test your results, try subtracting your value of $x$ from

`math.pi`

and see how
close to $0$ you get.