/sci/ - Science & Math » Thread #14118471

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Anonymous Tue 18 Jan 12:27:23 2022 No.14118471 View Reply Original Report

Quoted By: >>14118479 >>14118486 >>14118487 >>14118490 >>14118515 >>14118666 >>14118697 >>14118720 >>14118897 >>14120688 >>14120839 >>14121420 >>14123297

If you take a square root of 100+10^-50, the digits make a funny triangle shaped pattern. Why does this happen? It happens for all 100+10^n where 'n' is any negative integer.

Anonymous

Anonymous Tue 18 Jan 2022 12:30:44 No.14118479 Report

Quoted By: >>14118485

>>14118471
I'd tell you but my calculator doesn't do 10^-50. What is this bullshit?

Anonymous

Anonymous Tue 18 Jan 2022 12:33:12 No.14118485 Report

Quoted By: >>14118525 >>14120589

>>14118479
Only Finnish calculators can handle this.

Anonymous

Anonymous Tue 18 Jan 2022 12:33:37 No.14118486 Report

Quoted By: >>14118492 >>14120721

>>14118471
just change the width of ur window and it'll go away

Anonymous

Anonymous Tue 18 Jan 2022 12:33:46 No.14118487 Report

Quoted By: >>14122277

>>14118471
Sometimes nature creates funny patterns. See: Conway’s game of life

Anonymous

Anonymous Tue 18 Jan 2022 12:35:30 No.14118490 Report

Quoted By:

>>14118471
Because you masturbate to scat porn despite your mother repeatedly telling you not to.

Anonymous

Anonymous Tue 18 Jan 2022 12:36:09 No.14118492 Report

Quoted By: >>14118507 >>14118509 >>14118539

>>14118486
>just change the width of ur window and it'll go away
The pattern will still be there.

Anonymous

Anonymous Tue 18 Jan 2022 12:41:56 No.14118507 Report

Quoted By: >>14118520 >>14118566

>>14118492
can you post an example?

Anonymous

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Anonymous Tue 18 Jan 2022 12:44:02 No.14118509 Report

Quoted By: >>14118520 >>14123501

>>14118492
>The pattern will still be there.
>triangle shaped pattern

Anonymous

Anonymous Tue 18 Jan 2022 12:47:25 No.14118515 Report

Quoted By:

>>14118471
something close to this
https://www.youtube.com/watch?v=daro6K6mym8

Anonymous

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Anonymous Tue 18 Jan 2022 12:49:26 No.14118520 Report

Quoted By: >>14120031

>>14118507
>>14118509
Are you two actually retarded? Laying it out as a triangle helps visualize the pattern OP found, but it's obviously there regardless of how you lay it out: you'll still have these alternating runs of 9's and 0's, their lengths are still going to diminish in a predictable way, the space between them is still going to grow in a predictable way.

Anonymous

Anonymous Tue 18 Jan 2022 12:51:05 No.14118525 Report

Quoted By:

>>14118485
Tell me what you used to get such high precision so we could play around with it. There's no way anyone is figuring it out just from that one instance...

Anonymous

Anonymous Tue 18 Jan 2022 12:58:46 No.14118539 Report

Quoted By:

>>14118492
no it won't

Anonymous

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Anonymous Tue 18 Jan 2022 12:59:16 No.14118541 Report

Quoted By:

Here's square root of 100+10^-200 in base-20. The pattern seems to still be there but the triangle is now a lot flatter.

Anonymous

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Anonymous Tue 18 Jan 2022 13:06:32 No.14118558 Report

Quoted By: >>14118576

Here's square root of 100+10^-50 in base-20 (the 100+10^-50 also being in base-20). The pattern seems to work in different bases. Here I have two triangles but if I adjusted the window length it would make just one big triangle.

Anonymous

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Anonymous Tue 18 Jan 2022 13:08:40 No.14118566 Report

Quoted By: >>14121025 >>14121180

>>14118507
10.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000624999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999609375000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000273437499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999794921875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000161132812499999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999869079589843750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000109100341796874999999999999999999999999999999999999999999999999999999999999999999999999999999999999999907264709472656250000000000000000000000000000000000000000000000000000000000000000000000000000000000000080089569091796874999999999999999999999999999999999999999999999999999999999999999999999999999999999999929921627044677734375000000000000000000000000000000000000000000000000000000000000000000000000000000000061992406845092773437499999999999999999999999999999999999999999999999999999999999999999999999999999999944649636745452880859375000000000000000000000000000000000000000000000000000000000000000000000000000000049815326929092407226562499999999999999999999999999999999999999999999999999999999999999999999999999999954854859970510005950927734375000000000000000000000000000000000000000000000000000000000000000000000000041161745321005582809448242187499999999999999999999999999999999999999999999999999999999999999999999999962268400122411549091339111328125000000000000000000000000000000000000000000000000000000000000000000000034752789360936731100082397460937499999999999999

Anonymous

Anonymous Tue 18 Jan 2022 13:11:45 No.14118576 Report

Quoted By:

Oh wait a minute, it doesn't work in base-19. t. >>14118558

Anonymous

Anonymous Tue 18 Jan 2022 13:14:10 No.14118583 Report

Quoted By: >>14118605 >>14118697 >>14118853 >>14118922

OP here. Alright, so what I discovered is that the pattern only works in base-n where 'n' is an even number. That's interesting.

Anonymous

Anonymous Tue 18 Jan 2022 13:18:03 No.14118596 Report

Quoted By: >>14120721

for any random string thats long enough, there will be a window width that presents a pattern of some sort.

Anonymous

Anonymous Tue 18 Jan 2022 13:21:04 No.14118605 Report

Quoted By:

>>14118583
Try n^2+n^-50 for a couple of n

Anonymous

Anonymous Tue 18 Jan 2022 13:50:37 No.14118666 Report

Quoted By:

>>14118471
if you do 100 - 10^n instead and subtract it from 10 it cleans out the ...99999999... sections

then you get 5, 125, 0625, 0390625, 02734375, 0205078125, 01611328125, 013092041015625, 0109100341796875, 009273529052734375.... interspersed with zeros

like some sort of rational approximation but the fractions don't seem to follow any nice pattern.

1/2^1, 1/2^3, 1/2^4, 5/2^7, 7/2^8, 21/2^10, 33/2^11, 429/2^15...

Anonymous

Anonymous Tue 18 Jan 2022 13:59:20 No.14118685 Report

Quoted By:

https://oeis.org/A098597
>odd part of the nth catalan number
hmm

Anonymous

Anonymous Tue 18 Jan 2022 14:07:43 No.14118697 Report

Quoted By:

>>14118471
>>14118583
You’re observing some sort of rounding entropy into randomness, I guess. Interesting pattern

Anonymous

Anonymous Tue 18 Jan 2022 14:21:16 No.14118720 Report

Quoted By: >>14123291 >>14123551

>>14118471
Cute. It's a bit simpler to analyze if you look at 1+10^-50.
Look up the Taylor series for sqrt(1+x), it starts with lots of nice and quickly terminating fractions as coefficients (in even bases). And since your x=10^-50 is very small, you can reproduce those first few coefficients (.5, .125 or .875, .625, etc.) almost exactly in the decimal expansion, leading to the long strings of 0s / 9s.
The triangle gets smaller because the decimal expansions of the coefficients get longer, so you get fewer and fewer 0s / 9s until you get to the next one.

Anonymous

Anonymous Tue 18 Jan 2022 15:14:57 No.14118839 Report

Quoted By:

using catalan from above it looks like op's pattern can be generalized to

$\sqrt { b ^ { 2 } + b ^ { - n } } \; = \; b \; + \; \sum _{ x = 1 } ^ { \infty } \frac { ( - 1 ) ^ { x - 1 } \; \binom { 2 x - 2 } { x - 1} } { x \; 2^{ 2 x - 1 } \; b^{ ( 2 + n ) x - 1} }$

where b is the base (10 in op) and n is the spread (50 in op)

Anonymous

Anonymous Tue 18 Jan 2022 15:17:47 No.14118853 Report

Quoted By:

>>14118583
how do we know the computer is doing accurate calculations?

Anonymous

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Anonymous Tue 18 Jan 2022 15:35:35 No.14118897 Report

Quoted By:

>>14118471
This has to be related to rule 30

Anonymous

Anonymous Tue 18 Jan 2022 15:43:23 No.14118922 Report

Quoted By:

>>14118583
maybe because it's the square root? try it with cube root

Anonymous

Anonymous Tue 18 Jan 2022 20:34:13 No.14120031 Report

Quoted By: >>14120465 >>14123605

>>14118520
He called it a triangle shaped pattern. The triangle will no longer be there if you alter the width. If you don't care about it being a triangle and say it's about being a diminishing sequence pattern, then don't call it a triangle pattern.

Anonymous

Anonymous Tue 18 Jan 2022 22:14:20 No.14120465 Report

Quoted By:

>>14120031
>The triangle will no longer be there
retard

Anonymous

Anonymous Tue 18 Jan 2022 22:54:59 No.14120589 Report

Quoted By:

>>14118485
or bc

Anonymous

Anonymous Tue 18 Jan 2022 22:56:14 No.14120595 Report

Quoted By:

A:

This is called the Central Limit Theorem and is true for most large random variables. It has many applications.
In this case, the random variable is $X_n=10^{-n}$, and the Central Limit Theorem tells us that $$\sqrt{n}\cdot(10^{-n}-\frac 1{10^n})$$ is distributed as $N(0,1)$, which is the normal distribution.

A:

This happens because $X_n=10^{-n}$ is a non-negative random variable with finite mean $\mu=\mathbb E(X_n)=10^{-n}+10^{-n}=10^{-n}$. Now the Central Limit Theorem tells you that, as $n \to \infty$,
$$
\sqrt{n}\cdot(X_n-\mu)=\sqrt{n}(10^{-n}-\mu) \to \mathcal N(0,\sigma^2)
$$
where $\mathcal N(0,\sigma^2)$ is a normal distribution

Anonymous

Anonymous Tue 18 Jan 2022 23:18:55 No.14120688 Report

Quoted By: >>14120694

>>14118471
I don't know how rational numbers in digits, such as base 10 really work, so I can't even tell you why sqrt(1.1), sqrt(1.01), 1.001 etc has that pattern. Or 101, 1001, 10001 etc

Anonymous

Anonymous Tue 18 Jan 2022 23:21:16 No.14120694 Report

Quoted By:

>>14120688
I meant "real numbers"

Anonymous

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Anonymous Tue 18 Jan 2022 23:28:11 No.14120721 Report

Quoted By: >>14120993 >>14121025

>>14118486
this
hysterics losing their shit over a meaningless triangle unironically, math done on the same superstitious level as astrology.
and the cringoids have no self awareness at all, they can't see how ridiculous they're being "i'm a super smart genius, i don't make mistakes" is the only context they can view reality in

>>14118596
probably true, but who cares except a bunch of losers with nothing more interesting going on than
>OMG TRIANGLE!!!!!1

Anonymous

Anonymous Tue 18 Jan 2022 23:54:25 No.14120839 Report

Quoted By: >>14121338

>>14118471
There's a fucking HEXAGON on SATURN

Anonymous

Anonymous Wed 19 Jan 2022 00:38:40 No.14120993 Report

Quoted By:

>>14120721
>check 'em poster deriding people interested in a pattern

Anonymous

Anonymous Wed 19 Jan 2022 00:47:41 No.14121025 Report

Quoted By: >>14121180

>>14120721
see the webm in
>>14118566
the pattern exists regardless of the window

Anonymous

Anonymous Wed 19 Jan 2022 01:16:59 No.14121180 Report

Quoted By: >>14121508

>>14118566
>>14121025

It makes for mildly interesting imagery but it is unlikely to contain the secrets to the universe

Anonymous

Anonymous Wed 19 Jan 2022 01:51:46 No.14121338 Report

Quoted By:

>>14120839
https://www.youtube.com/watch?v=VQzLY17ncWM

Anonymous

Anonymous Wed 19 Jan 2022 02:09:29 No.14121420 Report

Quoted By: >>14121455

>>14118471
I'm betting on truncation errors. What is the chance that OP knows how to do arbitrary precision floating point operations? Especially considering he doesn't even use Linux.

Anonymous

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Anonymous Wed 19 Jan 2022 02:18:04 No.14121455 Report

Quoted By:

>>14121420
right, if the calculation isn't done by hand then there is no way to confirm if you're looking at a software error or a correct number.
the computer is just a black box to most users, they have no idea how or why it works, they just accept it on faith that the computer is an infallible god.
if you tell them something like
>pi starts to repeat after the 30th decimal place
they couldn't figure out if you're lying or not without asking the computer. they don't know how a computer calculates pi or how accurately and they're not capable of doing the calculation themselves, so its all just a leap of faith that the computer is infallible.

Anonymous

Anonymous Wed 19 Jan 2022 02:29:37 No.14121508 Report

Quoted By:

>>14121180
damn you think on a short enough timescale that that OP's observation is insignificant man that must suck

Anonymous

Anonymous Wed 19 Jan 2022 07:00:46 No.14122277 Report

Quoted By:

>>14118487
faggot

Anonymous

Anonymous Wed 19 Jan 2022 12:39:33 No.14123265 Report

Quoted By: >>14123267 >>14123282

>OP makes a mildly interesting observation that someone with moderate math education can easily explain
>most of the thread is people screeching about how it's fake / a numerical artifact / a Jewish conspiracy
Is everyone on this website retarded?

Anonymous

Anonymous Wed 19 Jan 2022 12:41:07 No.14123267 Report

Quoted By: >>14123289 >>14123300 >>14123356

>>14123265
You are watching recent vaxxoid reddit immigrants in action. It irrationally angers them when someone notices patterns and shows inquisitiveness.

Anonymous

Anonymous Wed 19 Jan 2022 12:44:27 No.14123282 Report

Quoted By: >>14123291

>>14123265
Explain it then, dimwit

Anonymous

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Anonymous Wed 19 Jan 2022 12:45:21 No.14123289 Report

Quoted By:

>>14123267

Anonymous

Anonymous Wed 19 Jan 2022 12:47:33 No.14123291 Report

Quoted By: >>14123306

>>14123282
See >>14118720
Expand the square root and it makes perfect sense.

Anonymous

Anonymous Wed 19 Jan 2022 12:49:14 No.14123297 Report

Quoted By: >>14123300

>>14118471
You just found a certain organization of data that gives you recognizable visual cues about the underlying thing, it's not magic and it doesn't mean anything. Best case scenario you can derive a formula to get a map to those number but that's it.

Anonymous

Anonymous Wed 19 Jan 2022 12:49:57 No.14123300 Report

Quoted By:

>>14123297
Perfect example of what >>14123267 said.

Anonymous

Anonymous Wed 19 Jan 2022 12:52:19 No.14123306 Report

Quoted By: >>14123318 >>14123339

>>14123291
Do the expansion and explain the triangle then. You can't, because you are just yet another /sci/ special snowflake narcissist bragging over nothing

Anonymous

Anonymous Wed 19 Jan 2022 12:54:51 No.14123318 Report

Quoted By: >>14123327

>>14123306
The absolute state of your mental illness...

Anonymous

Anonymous Wed 19 Jan 2022 12:56:26 No.14123327 Report

Quoted By: >>14123329

>>14123318
Wow you are such a genius. "Take the definition of the square root and you will see pattern". Go fuck yourself

Anonymous

Anonymous Wed 19 Jan 2022 12:57:32 No.14123329 Report

Quoted By: >>14123335 >>14123355

>>14123327
I'm not even that guy. I just find it remarkable how the average normaldrone's psyche is beginning to crack, and your crew is now lashing out at people for trying to figure out math problems.

Anonymous

Anonymous Wed 19 Jan 2022 12:59:04 No.14123335 Report

Quoted By: >>14123337

>>14123329
Sorry to break it to you, but you are the one talking like a schizo and make wild assumptions

Anonymous

Anonymous Wed 19 Jan 2022 13:00:00 No.14123337 Report

Quoted By: >>14123345

>>14123335
If there's any humanity left in you at all, try to do some self-reflection and ask yourself why you are angered by people noticing patterns and trying to fiure them out.

Anonymous

Anonymous Wed 19 Jan 2022 13:00:23 No.14123339 Report

Quoted By:

>>14123306
Please take your meds.
Look up the expansion of the square root around 1, write down the coefficients in decimal, and then look what happens when you multiply each of them by powers of 10^-50. It should be clear why you get lots of zeros and nines when you add up the results.

Anonymous

Anonymous Wed 19 Jan 2022 13:02:29 No.14123345 Report

Quoted By: >>14123347

>>14123337
I'm not, I'm angered by presumptous idiots derailing a thread with petty accusations while offering nothing of substance to the discussion

Anonymous

Anonymous Wed 19 Jan 2022 13:03:08 No.14123347 Report

Quoted By: >>14123351

>>14123345
I hope you get the treatment you need, and stick to websites more appropriate for your kind.

Anonymous

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Anonymous Wed 19 Jan 2022 13:05:33 No.14123351 Report

Quoted By: >>14123354

>>14123347
Go back, you are not welcome here

Anonymous

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Anonymous Wed 19 Jan 2022 13:07:09 No.14123354 Report

Quoted By:

>>14123351
>n-n-no u!

Anonymous

Anonymous Wed 19 Jan 2022 13:07:19 No.14123355 Report

Quoted By: >>14123356

>>14123329
can you imagine how facepalmingly cringey someone has to be to get excited about naturally occurring ascii art triangles?
>eureka!
>i discovered triangles!!
>this has got to be important!
doing math via ascii art numerology isn't a valid technique, its superstition, theres no possible proof of it's validity, this is an /x/ thread unironic

Anonymous

Anonymous Wed 19 Jan 2022 13:08:11 No.14123356 Report

Quoted By:

>>14123355
See >>14123267
You and other normaldrones are completely losing it.

Anonymous

Anonymous Wed 19 Jan 2022 14:14:26 No.14123501 Report

Quoted By:

>>14118509
cute dog

Anonymous

Anonymous Wed 19 Jan 2022 14:29:51 No.14123551 Report

Quoted By:

>>14118720
That's interesting. Still fancy pattern by the OP.

Anonymous

Anonymous Wed 19 Jan 2022 14:45:55 No.14123605 Report

Quoted By:

>>14120031
Jesus you really are retarded. gtfo of this board /fit or /pol might be more suitable for you.

Anonymous

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Anonymous Wed 19 Jan 2022 17:26:26 No.14124184 Report

Quoted By:

Nice discovery, part because the triangle is cool and part because you're somehow making people seethe over it (???)

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