/sci/ - Science & Math » Thread #12470129

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Anonymous Tue 15 Dec 23:26:44 2020 No.12470129 View Reply Original Report

Quoted By: >>12470151 >>12470161 >>12470315 >>12470351 >>12476184 >>12477675 >>12478500

Is $sin(e)$ algebriac?

Anonymous

Anonymous Tue 15 Dec 2020 23:31:33 No.12470151 Report

Quoted By: >>12475265

>>12470129
Define the function sin
Define the variable e... is it an array? Can you represent it in C for me?

Anonymous

Anonymous Tue 15 Dec 2020 23:32:29 No.12470161 Report

Quoted By: >>12470189

>>12470129
Don't ask shit that has a real academic focus on it. Look for obscure shit that's on the edge so it's not an eternity of jerking around and we get some answers.

Anonymous

Anonymous Tue 15 Dec 2020 23:36:14 No.12470189 Report

Quoted By:

>>12470161
I just thought it was interesting, maybe not necessarily related to anything relevant.

Anonymous

Anonymous Wed 16 Dec 2020 00:02:54 No.12470315 Report

Quoted By: >>12470340

>>12470129
highly unlikely. Sine on its own relies on pi, which is transcendental. You're working with 2 transcendentals here, a miracle has to happen for the result to be algebraic.

Anonymous

Anonymous Wed 16 Dec 2020 00:09:25 No.12470340 Report

Quoted By: >>12475269 >>12475870

>>12470315
But $e^{i\pi}$ is two transcendentals together to make an algebraic result.

Anonymous

Anonymous Wed 16 Dec 2020 00:12:45 No.12470351 Report

Quoted By:

>>12470129
no it’s clearly not
think of the base as it relates to th

Anonymous

Anonymous Wed 16 Dec 2020 00:24:05 No.12470386 Report

Quoted By: >>12471117 >>12473199 >>12473217 >>12475272

I can't find the theorem name right now, but it's known that unless you have sin(a*pi/b) for integer a,b it's transcendental.

Anonymous

Anonymous Wed 16 Dec 2020 00:49:42 No.12470493 Report

Quoted By:

I don't think it's known.

Anonymous

Anonymous Wed 16 Dec 2020 04:23:44 No.12471117 Report

Quoted By:

>>12470386
Niven's theorem?

Anonymous

Anonymous Wed 16 Dec 2020 13:19:11 No.12472182 Report

Quoted By:

No it's not. I can't think of a more irrelevant question.

Anonymous

Anonymous Wed 16 Dec 2020 19:17:50 No.12473199 Report

Quoted By:

>>12470386
trig function (rational multiple of pi) is algebraic which is well known, but what is the negation of this statement?

Anonymous

Anonymous Wed 16 Dec 2020 19:23:44 No.12473217 Report

Quoted By: >>12473561

>>12470386
Ok so now we ask, are there any integers a,b with pi/e = a/b?

Anonymous

Anonymous Wed 16 Dec 2020 20:07:00 No.12473427 Report

Quoted By:

yeah.
taylor polynomials man.

Anonymous

Anonymous Wed 16 Dec 2020 20:42:20 No.12473561 Report

Quoted By:

>>12473217
It would be quite surprising if pi/e was rational

Anonymous

Anonymous Thu 17 Dec 2020 07:26:37 No.12475265 Report

Quoted By: >>12477746

>>12470151
kill yourself faggot
sin is an elementary function and is known to everyone
e is a famous constant

Anonymous

Anonymous Thu 17 Dec 2020 07:27:46 No.12475269 Report

Quoted By: >>12475587

>>12470340
>i
you can't just make up numbers to solve problems
and even if you could, you can't just artificially insert them and dodge the question.

Anonymous

Anonymous Thu 17 Dec 2020 07:29:31 No.12475272 Report

Quoted By: >>12475862

>>12470386
It's known that the sine of a rational multiple of pi is algebraic, but it is not known that the sine of an irrational multiple of pi is transcendental

Anonymous

Anonymous Thu 17 Dec 2020 11:03:04 No.12475580 Report

Quoted By:

I think it should be possible to prove with a combination of the Lindemann–Weierstrass and Gelfond–(((Schneider))) theorems. Gonna give it a crack just cause I'm bored...

Anonymous

Anonymous Thu 17 Dec 2020 11:05:24 No.12475587 Report

Quoted By:

>>12475269
God I hope this is bait

Anonymous

Anonymous Thu 17 Dec 2020 13:13:29 No.12475862 Report

Quoted By: >>12476164 >>12478357

>>12475272
Surely sine takes algebraic multiples of pi exclusively to algebraic numbers and non-algebraic multiples of pi exclusively to non-algebraic numbers? Consider the inverse sine, how else could it possibly work?

Anonymous

Anonymous Thu 17 Dec 2020 13:17:59 No.12475870 Report

Quoted By:

>>12470340
This is actually how it's proved that pi is transcendental. If it were algebraic, so would by ipi, and then by Lindemann-Weierstrass e^ipi would be transcendental, contradiction.

Anonymous

Anonymous Thu 17 Dec 2020 15:16:00 No.12476164 Report

Quoted By: >>12476400

>>12475862
>inverse sine
Doesn't exist

Anonymous

Anonymous Thu 17 Dec 2020 15:19:32 No.12476184 Report

Quoted By: >>12476805

>>12470129
> $\sin()$
> $e$
> $\sin(e) = \frac{ie^{-ie}}{2}-\frac{ie^{ie}}{2}$
> $i$
> $e^{ie}$

Sorry but this is a board about science. Schizophrenic garbage goes to >>>/x/

Anonymous

Anonymous Thu 17 Dec 2020 16:28:42 No.12476400 Report

Quoted By: >>12476818

>>12476164
$sin^{-1}(x)$

Anonymous

Anonymous Thu 17 Dec 2020 18:39:13 No.12476805 Report

Quoted By:

>>12476184
Nigga what the fuck is this

Anonymous

Anonymous Thu 17 Dec 2020 18:42:52 No.12476818 Report

Quoted By:

>>12476400
Acting like every random string of nonsense means something
my refutation: afjka;lsdfj(

Anonymous

Anonymous Thu 17 Dec 2020 22:39:22 No.12477675 Report

Quoted By:

>>12470129
Engineer here.

We simply use the identity sin x = x

e is trancendental:
https://en.wikipedia.org/wiki/Transcendental_number#Sketch_of_a_proof_that_e_is_transcendental

Anonymous

Anonymous Thu 17 Dec 2020 22:58:32 No.12477746 Report

Quoted By:

>>12475265
It's called bait, sweety.

Anonymous

Anonymous Fri 18 Dec 2020 01:37:45 No.12478357 Report

Quoted By:

>>12475862
The most absurdly false claim made in this thread

Anonymous

Anonymous Fri 18 Dec 2020 02:41:45 No.12478500 Report

Quoted By:

>>12470129
no, it's real

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