Johnathan - 1 month ago 10

Python Question

I have an assignment where I need to approximate Pi in a computationally efficient manner. Here is my strategy: I use a unit circle, the angle bisector of an isoceles triangle, and the definition of sin. I drew a diagram:

For example, if I want to use an hexagon (6 points/6 sides), I simply need to compute

`a`

`0.5*sin(2*pi/2*x`

`2*x`

`Pi = Circumference/Diameter`

`Diameter = 1`

Essentially:

`from math import sin, pi`

def computePi(x): #x: number of points desired

p = x*sin(pi/x)

print(p)

computePi(10000)

3.141592601912665

It works, and I think it's as efficient as it gets, no? Thank you for your time!

EDIT: to avoid circularity, I'll compute sin(30) using a Maclaurin series. Then it should work.

Answer

Even better is

```
print(4 * math.atan(1))
```

This does not use pi in any obvious way in the calculation (though as @Jean-FranÃ§oisFabre comments, pi is probably used in the function definition), and in addition to the trig function it has just one simple multiplication. Of course, there is also

```
print(2 * math.acos(0))
```

and

```
print(2 * math.asin(1))
```