Pi Approximation Day

[Thomas Klemm]

(07-25-2022 12:03 AM)Albert Chan Wrote:  3 SQRT 2 +               // cot(pi/12) ≈ 3.732
ENTER X^2 1 + SQRT +     // cot(pi/24) ≈ 7.596
ENTER X^2 1 + SQRT +     // cot(pi/48) ≈ 15.26
ENTER X^2 1 + SQRT +     // cot(pi/96) ≈ 30.55
1/X

Now we're close enough to 0 that using only the first two terms of the Taylor series of the \(\arctan(x)\) function gives a good approximation for \(\pi\):

\(
\begin{align}
\arctan(x)\approx x-\frac{x^{3}}{3}
\end{align}
\)

So we can continue with:

ENTER ENTER X↑2 ×
3 ÷ -
96 ×

3.14159193225

---

Instead of:

ENTER X^2 1 + SQRT +

we could also use:

1 X<>Y →POL LASTX +