I made an infinite series for the approximation of pi but its inefficient, wondering how to optimize

[vital topaz]

https://www.desmos.com/calculator/y1ggqnjouk

[vital topaz]

Basically calculates the perimeter of the quarter circle and multiplies by two to get pi.

In the Desmos graph as you increase P, the approximation gets closer to pi

It’s kind of inefficient so I was wondering if there’s a way to optimise it while keeping the same idea

[ocean venture]

can you explain how you derived it?

[marsh elbow]

Idk but I made a approximation of pi using the area of a circle https://www.desmos.com/calculator/drdxna2ns5

[vital topaz]

Uh u get the sum of the distances between the points on the circle

And as N increases the distance between each point gets smaller

And there are more points

[marsh elbow]

So you are calculating pi through circumference

[vital topaz]

Yes

[vital topaz]

Welp yours seems better

[marsh elbow]

I tried to make one using arc length similar to what you did and I simplified it however it won’t calculate it because at 2 its 1/0

https://www.desmos.com/calculator/q2xnsqjruk

Time disappeared in a instant I have school in 5 hrs gn

[vital topaz]

Ripperoni

Welp I caused someone to have sleep deprivation

That's not good

[marsh elbow]

I would have anyway lol

Have you taken calculus?

[vital topaz]

No but anyway this is more for something I wanna try to computate with programming

And the arc length integral is the same as this I think anyways

[idle igloo]

hey wanna still try ot compute with programming

[vital topaz]

I alr did just saying its inefficient