/sci/ - Science & Math

yeah this is why I always found this identify to be overrated

this is fucking stupid. 1^(2*3) = 4 is true too if you come up with a retarded system for the values of your digits. people cream their pants over this identity because it contains so many famous mathematical constants. choosing to use degrees doesn’t nullify that, it just adds an invisible * (180 / pi) that you’d have to include if you actually wanted to fucking evaluate the equation

bro use variables and the general form of the fucking equation instead of your 5th grade meme equation and this doesn’t exist. fuck off
>>11902411
Brainlet

>>11902475
lol no. the identify doesn't look nearly as cool if you are not using radians which is a human-invented angle measuring system

>>11902383
This doesn't work though

Anon you forgot the degree sign

>>11902490
Every angle measuring system we use is human invented.

>>11902383
dangerously based

>>11902383
It’s actual exp((tau/2)*I)=-1
And exp(tau*I)=1

3^(3i) = -1

So beautiful

>>11902455
>>11902521
>>11902531
smoothbrains

>>11902383
e^(180 * i) =
-0.598460069 - 0.801152636 i

not really. radians are dimensionless.

I prefer e^0 = 1 because I don't like non-existent numerical abstractions

The exponential is defined by its power series, so [eqn]e^{180i} = \sum_{n=0}^\infty \frac{(180i)^n}{n!}\ne -1.[/eqn]

>>11902684
e^(180 * i) = e^((180-56*pi) * i)

>>11902730
Kek

>>11902624
Flammable

NJ Wildberger led me realise that Euler's identity is a scam.

>>11903585
NJ Wildberger is a brainlet

>>11902383
>>11902411
>>11902455
>>11902475
>>11902490
>>11902521
>>11902531
>>11902539
>>11902543
>>11902614
>>11902624
>>11902658
>>11902684
>>11902693
>>11902730
>>11902739
>>11903262
>>11903293
>>11903570
Can somebody explain why pi is used for angles? Why “pi/4” and not just “1/4”, or even better make a full rotation “1” and so “pi/4”=“1/8”

>>11903595
Because radians are equivalent to arc length on the unit circle.

>>11903621
That’s a non-answer

>>11903621
You referred to the definition in the definition

>>11903682
>>11903690
pi was defined in relation to the radius when it was created, where pi multiplied by r2 was the area and 2r was he circumference

>>11903595
>Can somebody explain why pi is used for angles?
because its natural, just take calculus and youll see why

>>11903595
it's the only constant such that sin(x) and cos(x) differentiate to each other

>>11902624
my eyes! MY EYES HURT!!

powerful...

>>11904384
which is why radians are the only correct system bait poster don't fucking you me

>>11902684
Op Btfo'ed along with the low iq shills itt

>>11902383
Are you retarded? Judging by the filename you're just here to shitpost, but its obvious that [math] \sin(180^\circ)[/math] is undefined since sine and cosine cannot input values with units. Underlying all your operations with degrees is a conversion factor, say, [math] c = \frac{\pi}{180^\circ}[/math]. So when you say [math]\sin(180^\circ) [/math] what is implicitly meant is [math]\sin(c\cdot 180^\circ) [/math] which is the same thing as [math]\sin(\pi) = 0[/math]

Also that is far from the "most beautiful equation." For me is has to be euler's other equation [math] \frac{\pi^2}{6} = \sum_{n=1}^{\infty} \frac{1}{n^2} [/math] which easily generalizes to the Riemann zeta function for even values

>>11903595
taylor expand sin(x) and cos(x), 2*pi pops out naturally as the period for those functions. taylor expand e^(i x) and you'll see why pi is the constant in Euler's identity. btw, we really should have defined 2 * pi as tau and used that

>>11905711
The ° IS the pi/180

>>11905662
>I have no argument

[math]\sqrt[\pi+e]{(\pi+e)^{\pi/e}} \approx 1.41[/math]

Of course it's valid.

180 = 60 * pi

>>11907391
Based engineer

e^πi = -1

>>11903595
try studying math buddy

>>11905680
>t. wolfram alpha

>>11902383
ps. your 180 formula is shit, too

Now the choice of units really is arbitrary (so long as units ∈ {degrees, radians}):

octave:1> exp(i*66178620)
ans = -1.0000000000 - 0.0000010462i
octave:2> exp(i*2*pi/360*66178620)
ans = -1.0000e+00 - 7.3808e-12i

>>11908614
>octave
ok retard

>>11903690
>>11903595
Pi was defined 2500 years ago by the ancient Greeks as the ration of the diameter of the circle to its circumference. A radian is a section of the circumference equal to the length of the radius. The radius is half the diameter, so there are 2pi radians in a circle.

>>11907391
close enough

>>11902383
numbers are dimensionless.

>>11912440
wrong

>>11902383
To be honest, as a graduated math major I still have no idea what people mean by "mathematical beauty" anyway.

E^pij plus 1 = -E^zero

>>11912448
[math] 1 + i \pi - \pi^2/2 -i \pi^3/6 + \pi^4/24 + \ddot = -1 [/math] is a pretty cool relationship

[math]\int_{-\infty}^\infty e^{-{x^2}}dx = \sqrt{\pi}[/math]

Stay mad

>>11902684
This. Op thinks e^x literally means taking e and multiplying it for itself x times lmao

>>11902383
That equation is wrong though

>>11912448
What attracts you to math then?

>>11912659
Transcendental numbers are cool.
1/1! + 1/2! + 1/3! + 1/4! + ... = e

>>11913003
fun fact
de/d1 = e

>>11902739
>>11905662
>>11903621
>>11913003
>>11913003
list of reason why op is a gay

>>11903595
If one measures angles by the arc length they sweep out on a circle and defines the circumference as a multiple of the radius then pi falls out naturally since it is the a multiple of the ratio of radios to circumference

>>11903595
>make a full rotation “1”
That's called tau, bro

>>11915966
redefine the diameter as a new constant = 1/tau

>>11917438
Bruh, tau = 2*pi. You don't need to redefine anything.

>>11902383
Yes, using intentionally terrible notation makes normally beautiful equations confusing and ugly. Why are you stupid enough to believe that this is news?

I wish I could strangle every single mathematician

Obviously if you change units formulae will change. Do you think this is some earth shattering revelation

>>11902739
op rekt

All this identity says is that if you rotate 1 a half circle around the origin, you get -1. The exponential function scales and rotates. There's nothing "beautiful" about it, only mathlets think this identity is interesting.

This is why Gauss thought that anyone that was impressed by it was retarded and would never go far in mathematics; he was totally right.

>The mathematician Carl Friedrich Gauss was reported to have commented that if this formula was not immediately apparent to a student upon being told it, that student would never become a first-class mathematician.

>>11912448
Getting a math degree doesn’t cure autism or temporal lobe deficits, it just makes them worse.

Choice of units is not arbitrary. The exponential function only takes a dimensionless argument. Radians are dimensionless. Degrees have dimension denoted bu the little superscript degree symbol.