Continued Fraction Pi | Mathematics | Page 1

trim hazelBOT Feb 19, 2025, 4:34 AM

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shadow stone Feb 19, 2025, 4:35 AM

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Also another question, how in the world does this work

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the arctan makes sense

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but mine dosent seem like arctan

wispy siren Feb 19, 2025, 4:42 AM

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3.14234234234 = π ?

shadow stone Feb 19, 2025, 4:45 AM

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wispy siren 3.14234234234 = π ?

no it approaches pi

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see the website

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it has a playground

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to test

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it

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this is another continued fraction, but its not as fast as mine

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not sure how these work

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thats why im confused

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23 terms already is very accurate

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or precise

shadow stone Feb 19, 2025, 5:04 AM

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I cant get a clear answer

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anywhere

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i hope some of u can like

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help

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what does this have to do with a circle

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even chatgpt

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isnt helping

shadow stone Feb 19, 2025, 7:00 AM

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e

potent tartan Feb 19, 2025, 7:01 AM

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what exactly is your confusion here

shadow stone Feb 19, 2025, 7:03 AM

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what does that fraction thing

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have to do with circles

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how

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not what

potent tartan Feb 19, 2025, 7:06 AM

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i don't necessarily agree with that sentiment

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like the idea pushed by 3b1b, that every instance of pi is related to a circle

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it's probably true, but sometimes it's kind of a waste of time trying to find some kind of connection a circle

shadow stone Feb 19, 2025, 7:08 AM

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yeah i agree

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but humans are like that

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we want to understand things using what we already know

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and thats waht i wanna do

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so i can intuitively know whats happening

potent tartan Feb 19, 2025, 7:11 AM

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well, an answer would be that arctan(1) = pi

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and that the taylor series of arctan is universally convergent, i.e. its continued fraction form at x=1 will approximate pi

shadow stone Feb 19, 2025, 7:12 AM

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arctan 1 is pi/4

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but is that arctan continued frac?

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when i tried googling i got a ton of stuff

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this

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and this

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none were what i was doing

candid oracle Feb 19, 2025, 3:41 PM

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so the website tells you a number that's close to pi?

shadow stone Feb 19, 2025, 11:04 PM

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candid oracle so the website tells you a number that's close to pi?

it uses the continued fraction thing i made

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to approximate

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it generates pi

misty glacier Feb 20, 2025, 12:43 PM

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Both of these formulas are well-known and can be found on Wikipedia. The first one is from the article about tanh(x), and it does not converge to pi. The second one is from the article about pi. Both can be proved from differential equations.

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The first one converges to 4-8/(1+e²)

shadow stone Feb 20, 2025, 1:04 PM

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misty glacier Both of these formulas are well-known and can be found on Wikipedia. The first o...

huh

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okay

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i tried finding one

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and i got the first one

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🤷‍♂️

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thx tho

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but also what does it have to do with circle

misty glacier Feb 20, 2025, 1:09 PM

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shadow stone but also what does it have to do with circle

The connection is rather lengthy. Generally it goes through derivatives of trig functions. Like arctan(x)'=1/(1+x²)

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And trig functions do have something to do with a circle 🙂

shadow stone Feb 21, 2025, 12:03 AM

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huh

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okay

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yeah i understand the arctan relationship to circles

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the thing im confused is what does a fraction and trig have to do with each other

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i mean like i know trig is just ratios

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but expanded infinite ones?

#Continued Fraction Pi