/sci/ - Science & Math » Thread #11963879

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Anonymous Sun 02 Aug 16:19:06 2020 No.11963879 View Reply Original Report

Quoted By: >>11963895 >>11968156 >>11968180

It's a fact that the length of the circumference of a circle is equal to its radius times an irrational coefficient. But why? Why isn't Pi a rational number instead? Why does the universe have to work in this particular way?

Isn't Pi also exactly equal to 1/3 - 1/5 + 1/7 - 1/9 + 1/11 - 1/13... or something like that? How does that make sense?

Anonymous

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Anonymous Sun 02 Aug 2020 16:28:23 No.11963895 Report

Quoted By: >>11963907

>>11963879
Indeed, I've been wrestling with this myself lately. Like Buckminster Fuller's views on the irrationality of pi summed up well in http://www.arvindguptatoys.com/arvindgupta/synergy-fuller.pdf

chapter 2

How many digits of pi will nature attempt to calculate before she gives up and procures a fake bubble. No, Bucky is right, nature isn't using pi. And i have an ear open to the scientific-esoterics who believe that pi has a natural end in natures calculator.

irrationality and the ... and so on so forth operator make rich and elegant metaphysical maths, but not one that is evoked easily in nature

Anonymous

Anonymous Sun 02 Aug 2020 16:31:29 No.11963907 Report

Quoted By: >>11964354 >>11966508 >>11968160

>>11963895
So, I'm pretty sure Pi is proven to be a real thing, so is nature "creating" digits of Pi or are people just discovering more digits as they find better ways to understand it...?

And conceptually, an irrational number is like infinity, we can't ever reach the end, no matter what we do... so pi is an impossible number to calculate the value of, we can only represent its value with different contexts but never express its value out of context.

Maybe its because Pi is fundamentally its own context and can't be translated into an irrational number, because it would never end, an instead, Pi exists only in its own context.

Also why is 1/3-1/5+1/7-1/9 also equal to exactly Pi? Or is it a fourth of pi actually?

I think pi/4 = 1/3-1/5+1/7-1/9 or something similar to that at least... I don't remember...

What the...

Is there a universe that can exist where Pi is actually a rational number?

Anonymous

Anonymous Sun 02 Aug 2020 18:01:30 No.11964354 Report

Quoted By:

>>11963907
> Also why is 1/3-1/5+1/7-1/9 also equal to exactly Pi? Or is it a fourth of pi actually?
It's ?/4=1-1/3+1/5-1/7+..., Leibniz formula.

Note that this is just the result of setting x=1 in the Taylor series for arctan x:
arctan x = x - x^3/3 + x^5/5 - x^7/7 + ...

Anonymous

Anonymous Sun 02 Aug 2020 20:38:43 No.11966508 Report

Quoted By:

>>11963907
Fucking schizo

Anonymous

Anonymous Mon 03 Aug 2020 03:54:21 No.11967906 Report

Quoted By:

The fact here is that true circles aren't real.

Anonymous

Anonymous Mon 03 Aug 2020 05:45:37 No.11968147 Report

Quoted By:

Historically the first proof that ? was irrational was by Lambert and makes use of a continued fraction. I don't know where the continued fraction formula came from...

Later on Lindemann prooved that ? was also transcedental (can't be made with compass and straightedge, unlike ?2).

* https://www.quora.com/How-do-you-prove-that-pi-is-an-irrational-number
* https://mathscholar.org/2018/09/simple-proofs-the-irrationality-of-pi/
* https://proofwiki.org/wiki/Pi_is_Irrational

Anonymous

Anonymous Mon 03 Aug 2020 05:51:18 No.11968156 Report

Quoted By:

>>11963879
How many universal constants are rational? Is the speed of light? The Plank time constant? They are all just ratios of different things, and those ratios aren't convenient integer relationships. Why should pi be different?

Anonymous

Anonymous Mon 03 Aug 2020 05:53:04 No.11968160 Report

Quoted By: >>11968180

>>11963907
Well, one interpretation of pi is that it is the measure of the curvature of space in this universe. If so you could conceive of an alternate universe where pi has a rational value.

Anonymous

Anonymous Mon 03 Aug 2020 05:56:36 No.11968169 Report

Quoted By:

>How does that make sense?

$y = \log(1-x) = \int^x \frac{1}{1-x} = \int^x \sum_{k} (-t)^k dt = \sum_{k} \frac{(-t)^k}{k}$
(note the pattern you ask for)
is the inverse of $1-\exp(y)$ , which relates to $\pi$ via the famous Euler formula.

So the answer is essentially "through the geometric simplicity of the exponential function"

Anonymous

Anonymous Mon 03 Aug 2020 06:00:23 No.11968180 Report

Quoted By:

>>11963879

>How does that make sense?

$\log(1-x) = \int^x \frac{1}{1-t} dt = \int^x \sum_{k} (-t)^k dt = \sum_{k} \frac{(-t)^k}{k}$
(note the pattern you ask for)

is the inverse of $1-\exp(y)$ , which relates to $\pi$ via the famous Euler formula.

So the answer is essentially "through the geometric simplicity of the exponential function"

>>11968160
"universal constants" are a meme and moreover you're conflating interesting numbers with physical constant.
The former are just particular numbers, with some usually straight forward algorithm to computer them.
The second are reference values that get introduced per new unit when a formula that relates measurable quantities is elevated to be part of a physical theory - they are framework dependent (and physical realism is a shaky ontology anyway).

Anonymous

Anonymous Mon 03 Aug 2020 06:13:15 No.11968208 Report

Quoted By:

Why should the universe be bound by the conventions of human thought?

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