For me it's MegAdeTH

>>16437003
You didn't give the whole question retard

What are the best nootropics and supplements to bolster my acuity?
I trust you all more than /fit/.

>>16437155
caffeine and a good night's sleep

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How many possible are combinations are there in a pentagram? I want to know how many shapes there are in here. Considering pic related is also a shape

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Can it be solved?

>>16437887
i have a marvelous proof of the case of n=2, which is too long to fit in this post.

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>>16437887

>>16437887
>inside a circle
Do circles have an inside? (They definitely have no interior.) BTW, for n=2,3 probability is 0.

There are infinite points in a circle. A probability cannot be calculated.

>Let [math]A\subset \chi(\mathbb{R}^3)[/math] be a subspace with basis [math]\{X,Y,Z\}[/math] where [math]X = y\partial_z - z\partial_y \,,\, Y =z\partial_x - x\partial_z \,,\, Z = x\partial_y - y\partial_x[/math]
Help me understand this. What is [math]\chi(\mathbb{R}^3)[/math]? Why were the basis vectors written as partial derivatives?

>>16438258
>What is χ(R3)
You could easily check on ChatGpt
>χ(R3) can denote the space of compactly supported smooth functions...

>Why written like that
Cause if you play around with them you notice you get rotations.

Those are some constant multiple of the angular momentum operators. Instead of X,Y, and Z, think of L_z, L_y, L_z, where angular momentum L = r X p, where p_x = hbar/i * d_x. That multiple hbar/i doesn't really matter. The space of these Hermitian Operators (so they represent an observable) are a Lie algebra for the generators of rotation, so the exponential map of this algebra gives a Lie group representing spacial rotations. So similar to how momentum generates spacial translation, angular momentum generates spacial rotations via the exponential map.

By Fermat's last theorem you can not split a cube into two other cubes like a^3+b^3=c^3. But can the equation hold if there's more cubes, like a^3+b^3+c^3+...+n^3 = x^3?

>>16438598
2^3=1^3+1^3+1^3+1^3+1^3+1^3+1^3+1^3

>>16437553
define different
all n-sided shapes count only once for each n? e.g. a triangle is a triangle no matter the side lenghts
if not, does rotating count as a different shape?
are you maybe confusing your question with a graph related task?

>>16438598
Assuming all the integers are > 1 and unique, then the shortest counter-example would be: [math]3^3 + 4^3 + 5^3 = 6^3[/math]

>>16438624
Is it proven that you can do that sort of thing for every power, not just for a cube?

>>16438788
We have lots of examples for different powers up to 8 (not sure about higher) but is it not proven if you can do it for every power. For example no one has found any solutions if the power = 6.

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>>16436512
will analysis make me better at calculus and applying it and sheeit

>>16439272
Yes...that and two extra inches

If I have to prove that a subspace [math]A < \mathfrak{X}(\mathbb{R}^3)[/math] is a Lie subalgebra, do I really NEED to prove that it's closed under the Lie bracket? Is that the only way? Shit's getting messy over here.
For context, this is the problem:
>Let [math]A < \mathfrak{X}(\mathbb{R}^3)[/math] be the subspace with basis [math]X_1,X_2,X_3[/math] where [math] X_j = x^{\sigma(j)}\partial_{x^{\sigma^2(j)}} - x^{\sigma^2(j)}\partial_{x^{\sigma(j)}}[/math] and [math] \sigma = (1\,2\,3) \in S_3[/math]. Prove that [math]A[/math] is a Lie subalgebra of [math]\mathfrak{X}(\mathbb{R}^3)[/math]
The problem actually is a bit different at first (although my statement is equivalent to the OG statement), I just introduced some other notations and the permutation to make it more convenient and allow me to work under a summation sign.
I just took two vector fields [math] F_1 = \sum_{j}f_{1j}X_j\;,\; F_2 = \sum_{k}f_{2k}X_k[/math], put them both in the Lie bracket and then I'm just developing the algebra. The [math]f[/math]'s are functions in [math]C^\infty(\mathbb{R}^3)[/math].
Might work, but it's so fucking tiring and bothersome that there must be an easier way.
Any help is appreciated.

>>16436512
Im looking for that paper done by the black maths PhD student who wrote it like a nigger due to “avoiding eurocentric language”, anyone got the name?

>>16437887
Continuous domain? Approaches zero, effectively asking for (prob will have intersect lines)/(prob a it just doesn’t just sperg in a small area).

For discrete domains you could probably do something * resolution that covers all possible pixels of a circle (probably based on on the area).

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>>16436512
How come Hamas can take armed shepards and have them fly with a motorbike and a sheet aub we get stuck in traffic all the time?

>>16437887
Sounds like a clever variant of Bertrand's paradox.

>>16437887
>>16437887
P(n) = (2/3)^((n - 1)(n - 2)/2)
In the context of the problem, n represents the number of lines formed by connecting the sequentially chosen random points inside the circle. Since you start with one initial point and then select additional points, connecting each new point to the previous one, the total number of points will be n + 1, but the number of lines connecting them is n.
P represents the probability that none of the n line segments intersect each other.

>>16440154
>add length and girth with these simple equations
prove it.

>>16438614
each unique face as in each various rotation, im not sure if this is a graph task
anyway the number i came to was 282

>>16436512
any recommendation on what open source/free software to use to simulate electrodynamics? I am kinda sick of looking at formulas and never real world stuff. Was reading up on how to simulate microwave antennas but thats a bit over my head...

Why does the inner product have conjugate symmetry?

That is:

[math]<V|W> = <W|V>*[/math]

I'm coming at this as a physicist trying to understand Hilbert spaces. Conjugate symmetry is stated without proof in my notes/textbook. Is there some deep idea here, or an enforced property of Hilbert spaces?

>>16441119
it's so that the inner product of any wavefunction with itself is real, which lets you interpret it as a probability distribution

>>16441119
That comes from the fact / definition: [math]| A \rangle^{\dagger} = \langle A |[/math]

So [math]{\langle W | V \rangle}^{*} = (\sum_{i} W_{i}^{*} V_i)^{*} = \sum_{i} V_{i}^{*} W_i = \langle V | W \rangle[/math]

>>16441157
And for a continuous function, instead of a summation, it would be an integral

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what does a narrow height for normal distribution indicate?

>>16441488
I think you mean narrow width, not height. It means a small variance, so most of the values are distributed around the mean.

>>16441490
>I think you mean narrow width

man this shit is confusing sometimes. Thanks

>>16441026
ElmerFEM

What really is the distribution of vector fields?
I thought it was just the span of the vector fields but apparently that definition if only locally correct (whatever that means).
And also, the definition I'm using for vector field is that a vector field on a manifold [math]M[/math] is a linear map [math]X:C^\infty(M)\to C^\infty(M)[/math] that is also a derivation. Following from this definition, how can I define a covector field? A covector field is supposed to be a differential form, right?

I’m gonna get a 0 on my eletromag test

>>16443019
good. healthy people don't do STEM.

>>16436512
So I'm stuck in Analysis 1 again.
I can't figure out the next number in this sequence: 1, -7, 9, 119, ...
9 is the difference between 1 and -7, but I have no idea how they came up with 119, chatGPT tells me it's either 323 or 393 depending on whether I ask 4o or o1. Wolfram alpha told me to fuck off.

>>16443088
>chatgpt
>stem

tell me you're an overachieving midwit without telling me you're an overachieving midwit

>>16443113
>tell me you're an overachieving midwit without telling me you're an overachieving midwit
No shit anon, but I didn't ask for social commentary. Yes, I'm a midwit. Does that satisfy your superiority complex? Yes? Then help me with this please. Thanks
>Verification not required.

>>16443088
>9 is the difference between 1 and -7
Are you really, really, REALLY sure about it?

>>16443088
Try with 2, -6, 10, 120 and add -1 to the closed form

What is the electric magnetic field made out of?

>>16443581
It isn't made of anything. It's just a property at some point in space.

>>16443592
Whoa thats deep

>>16443592
Tell me more about this property you speak of

>>16443713
The electromagnetic four-potential.

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Could you give me ideas for my advanced lab final experiment? The lab mainly focus in thermal and material physics. It can't be something too long since we don't have many time to work on it.
Extra points if I could you a PID controller or a lock in amplifier on it.

>>16443719
>>16443719
>The electromagnetic four-potential.
This particular Absolute Nothing you speak of exists at points in space and posses properties?
Do go on

>>16436512
All I see is some fake ass stupid nails with the quick sticking out into nothingness. Can't these stupid bitches at least get nails that are somewhat realistic?

>>16443728
So what's a field anon?

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i saw this on /gee/. what do you think?

>>16443938
The answer is zero. Cut the image in half: the 40m cable + 10m height = 50m pole. So the cable can't be any other position except hanging vertically.

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>>16443938
Cables hang like hyperbolas.

>>16444109
Amazon would not ask their applicants to solve the catenary equation, there is always a trick to these kind of questions.

>>16444109
[[citation needed]]. I was learned that cables hang like cosh function.

>>16444114
Maybe something with a line integral because they give you the length of the cable.

>>16444170
Are you intentionally missing the point or just retarded?

>>16443945
Is this right? It sounds right.

>>16444175
The latter. Just noticed >>16444176

>>16444176
It's right. It's a well known question, just google it.

I am learning web dev which made me interested in going way deeper in learning programming, but to do that i would need to touch up on maths which
a) i wasn't particularly good at
b) haven't studied any math in like 10 years
what would be a good comprehensive place to relearn maths as much as i can?

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Which vaccines do you recommend/not recommend for a newborn? I'm a new dad and I'm really struggling with where to approach this whole subject. I figured /sci/ would be the best place to start. I intend on doing my own digging but I figured it wouldn't hurt to get some sort of foundation here. I greatly appreciate any advice with this.

Fag

If I have a 1-form [math]\omega[/math], what does it mean when it says [math]\mathrm{d}\omega = 0 \;\mathrm{modulo}\;\omega[/math]?

>>16443945
i'm retarded. why are you summing the height with the cable length?

>>16444350
I think you might have copied down the language incorrectly. Just post a screenshot of the context or something

>>16444432
I copied everything correctly. I have [math]\omega = -x^2x^3\mathrm{d}x^1 + x^3\mathrm{d}x^3[/math]. The problem at hand asks
>Verify if [math](\mathrm{d}\omega)|_\mathcal{D}[/math], i.e. if [math]\mathrm{d}\omega = 0 \text{ modulo } \omega[/math]
and I'm taking [math]\mathcal{D} = \langle\partial_{x^1}+x^2\partial_{x^3}\;,\;\partial_{x^2}\rangle[/math]

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Wtf, is it normal?

>>16443723
Lava batteries

>>16443932
>So what's a field anon?
A field can be many things, a field of grass, a field of wheat, a field for football, a field of air

I kind of understand the idea of the parts of atoms

I have experienced being struck by the light of the Sun

I kind of understand that atoms are made of something

So the first question in my convo here;

What is the electric magnetic field made of

>>16443938
If you tilt the 50 pole down it goes slightly across the half way point, this implies the full length is slightly less than 100

Lay down somewhere with the sun shining on you, and tilt your head at certain angles while squinting your eyes, you will notice rainbow effects of the light hitting your eyelashes, there is then a certain way to focus your eye and move it slightly and really focus it while slightly moving it around these rainbow visions, In which you will see what looks like small solid white circle, pin dot, surrounded by a thin circular line. Like a bulls eye, a gap, and then 1 circular band:

What are those?

>>16444360
Another way to think about it is subtract the height from the ground (10m) from the height of the pole (50m), this leaves you with a vertical height of the parabola = 40m. But that is the exact same length as half of the entire cable. So that can only be true if the cable is vertical.

>>16443932
>So what's a field anon?
It's a place where you can add, substract, multiple and divide (as long as you remember not to divide by zero!) Oh, and also distribute.

>>16444463
Looks like nonsense to me, since on its face the expression would seem to mean d\omega is proportional to \omega, but they are forms of different ranks.

Anyway here is someone with the same unanswered question:
https://math.stackexchange.com/questions/2327678/meaning-mod-and-differential-forms

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>>16436512
bros since we are all atheists who fucking love science i'm gonna ask this one: how do you avoid the christian to woketard pipeline? i'm scared it might happen to me

>>16444489
>Lava batteries
How is that a physics experiment?

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Do any math nerds know how to answer this question? It relates to the binomial and beta distributions, but I'm a bit lost as to how to use that connection to arrive at a solution and ChatGPT is no help.

>>16444947
You can prove it by induction (starting from r=n) and integrating the integral by parts.

>>16444988
Can you give me some idea on how to get started with that? I don't have a strong background in math.

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Please help me, /sci/. I don't know how to search this problem in google, because I get a lot of interference from similar sounding concepts that aren't quite what I'm looking for. Also, I'm a math retard, so I don't know how to read half of the results I receive.

Basically, I'm trying to find something like a weighted average between 3 or more points. I can do it with 2 points, but 3 or more, makes it too complex. I'm hoping the illustration gets the idea across. The 3 red points are static. The green point is one that you and I can control and move around.
1. When the green point is in the middle, the 3 red points average out evenly.
2. When the green point nears one of the red points, the nearest red point increase in value in proportion, and the others decrease in proportion.
3. When the green point overlaps one of the red points, it is now at maximum value, and the other points are at zero.
4. Same as 3, but now the green point overlaps a different red point. Showing that any point should be capable of assuming max value, and zeroing out the other points.

How can I do this?

>>16443945
The 40m of cable length and the 10ft to the hanging midpoint would overlap, akshully.

>>16444109
>>16444125
He's confused, because comparing the equations y=f(x) for each curve they are different [catenary is hyperbolic function and hyperbola is algebraic] but the parametric equations of the hyperbola does use both hyperbolic trigonometric functions

>>16445114
What??

>>16445040
Look at this animation
https://www.mathopenref.com/coordcentroid.html

>>16445186
This is not what I need. I'm already able to find the center of 3 points. Remember I said the red points are static? I don't need them to move. The green point moves. And then by moving the green point between the red ones, a new value is extracted. A value that shows the proportional distance between red and green.

>>16444526
>Lay down somewhere with the sun shining on you, and tilt your head at certain angles while squinting your eyes, you will notice rainbow effects of the light hitting your eyelashes, there is then a certain way to focus your eye and move it slightly and really focus it while slightly moving it around these rainbow visions, In which you will see what looks like small solid white circle, pin dot, surrounded by a thin circular line. Like a bulls eye, a gap, and then 1 circular band: What are those?

Anyone?

>>16445040
Let the red points be [math]P_1(x_1, y_1), P_2(x_2, y_2), \cdots[/math] and the green point be [math]P_0(x_0, y_0)[/math]
Then, calculate the distance from the green point to each red point as
[eqn]d=\{\sqrt{(x_1-x_0)^2+(y_1-y_0)^2},\cdots\}[/eqn]
where [math]d_n[math]
Then, the total distance is [math]d=\sum{d_n}[/math], and the proportions are
[eqn]d^*=\{\frac{d_0}{d},\cdots\}[/eqn]
which should be what you're looking for.

>>16445215
ah i'm a faggot for typing that shit out wrong but the last equation is just
[eqn]d^*=\{\frac{d_0}{d},\cdots\}[/eqn]

>>16444895
You said thermal. Set up a battery factory near a very thermal very safe volcanic site, to trap the energy in large batteries then ship them out

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>>16445215
>>16445216
>Let the red points be P1(x1,y1),P2(x2,y2),⋯ and the green point be P0(x0,y0)
ok

>Then, calculate the distance from the green point to each red point as
Alright.

>d={(x1−x0)2+(y1−y0)2−−−−−−−−−−−−−−−−−−√,⋯}
Not sure what that equation is, but I assume it's summing up the many distances from green to red.

>where dn[math]Then,thetotaldistanceis[math]d=∑dn
You lost me. What are you doing here? Can you explain the concept in plain terms? I'm barely math literate, and work better conceptually.

I should say that I can already get the proportions of the distances, if that's what you're doing. I add up the distances between red and green, and then divide the individual distances by the total. That's a way of getting proportions, but not the exact proportions I'm looking for.

>>16445234
>That's a way of getting proportions, but not the exact proportions I'm looking for.
oh i see what you want
just do d-d_n instead, i think you just want it inverted

>>16445234
okay i took another look at this and what i think you want is the absolute difference between the green point's distance to a red point, and the red point's distance to a red point

>>16445313
>just do d-d_n instead
What does d-d_n mean?

>>16445324
An absolute value is when you get the difference between two points, but it's always positive, right? How does that help? I can do that. But I'm not sure to what end.

>>16444481
Seems like you have an unusual personality.

>>16444263
Khanacademy. Also saw mathacademy.com shilled on hackernews but idk if it's worth the money
>>16444481
No, you're unusually autistic, but the data there might be skewed due to social desirability bias. You'll get more accurate results by combining self-evaluation with assessments from people who know you.
>>16444526
Maybe an Airy disk caused by a pinhole from intersecting eyelashes?
https://en.wikipedia.org/wiki/Airy_disk?useskin=vector
>>16444947
https://math.stackexchange.com/questions/624688
Here's for [math]X \leq r[/math], now try something similar
>>16445040
https://en.wikipedia.org/wiki/Barycentric_coordinate_system?useskin=vector

>>16445217
"Thermal physics is the combined study of thermodynamics, statistical mechanics, and kinetic theory of gases."

Is there any artificial sweetener with fluorine in chemical formula?

>>16446029
None come to mind.

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>>16445978
>https://en.wikipedia.org/wiki/Barycentric_coordinate_system?useskin=vector
Holy shit. That's what I'm looking for! And pic related, is actually what I'm trying to do! This is a great lead, thanks for the link. Now I know what it's called, I can get help on it. Unfortunately, I still have to try and work it out, which is going to be hard.

If anyone is feeling generous, I would appreciate an dumbed down explanation for how this works. In the mean time, I'll read on, and see what I can glean.

If I have a sphere and n points spread evenly across the sphere, how far apart are the points from their closest neighbor? I'm looking for an equation ideally or at least some simple way to approximate it.
A specific example: If I have a sphere that is 1 micron in radius and 600,000,000 points evenly distributed across the surface of the sphere, how far apart will a point be from its closest neighbor?

If I define a subspace [math]J^k(V)\leq \mathcal{T}^k(V)[/math] spanned by all tensor products [math]\bigotimes_jv_j[/math] of linearly dependent vectors [math]\{v_j\}_j\subset V[/math], can I define the exterior product [math]\Lambda^k(V^*)[/math] as the quotient [math]\Lambda^k(V^*) = \mathcal{T}^k(V)/J^k(V)[/math]?
Furthermore, considering the projection of [math]\mathcal{T}^k(V)[/math] onto [math]\mathcal{T}^k(V)/J^k(V)[/math], i.e., a map
[eqn]
\begin{align}
\pi:\mathcal{T}^k(V)&\to \mathcal{T}^k(V)/J^k(V)\\
T &\mapsto T + J^k(V)
\end{align}
[/eqn]
can I say that by restricting its domain to the subspace of skew-symmetric tensors I'll have an isomorphism?

>>16446507
There is no exact equation and it's actually an unsolved problem (the Tammes problem). However you can generate the points using some code like the Fibonacci sphere algorithm. As a *very* rough approximation you could cut the surface area of the sphere into N squares or smaller circles and then calculate the distance between them.

>>16446530
Oh wow. Okay thanks for the info. I guess the idea is if the region of the surface is sufficiently small, it's approximately flat and can be treated as 2 dimensional?
That works for me

w-what happened to The Phenotype pic in our sticky..

>>16446646
What do you mean?

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Brainlet here. I am confused about question c in pic rel. Why doesn't the argument for uncountable Omega work for countable Omega? In both cases, none of the infinite sets are disjoint, yet in the uncountable case, we can still include an infinite amount of finite sets.

When have you failed to reject your null hypothesis /sci/?

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I'm missing something and I don't know what

>>16444463
They're asking you to verify if [math] d \omega = \omega \wedge \alpha [/math] for some 1-form [math] \alpha [/math]

>>16446875
Legible handwriting is what you are missing.

Is there an equation that gives out the result of a degree n polynomial being differentiated n times?

>>16447431
>Is there an equation that gives out the result of a degree n polynomial being differentiated n times?
Unless it's a very, very tricky question, the result will be [math]a_n n![/math], where [math]a_n[/math] is coefficient by [math]x^n[/math].

>>16447447
Now that i look back at it, it was quite a stupid question. Thanks!

>>16447447
>Unless it's a very, very tricky question
nta but im curious for an example where this doesnt hold.

>>16447431
Same guy. Was wondering if this would also mean that:
y=(ax^n + bx^(n-1)....+z)^c
after differentiating n\cdot c times:
\frac{dy^(nc)}{d^(nc)x} = a^c \cdot (nc)!

>>16447560
Same guy. Was wondering if this would also mean that:
[math] y=(ax^n + bx^{n-1}....+z)^c [/math]
after differentiating n\cdot c times:
[eqn] \frac{dy^{nc}}{d^{nc}x} = a^c \cdot (nc)! [/eqn]

Note: im new to this board

>>16447575
Yes that's correct.

>>16447489
in a field with characteristic [math]p[/math] it will sometimes be zero

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i assume the distribution on the right is a better fit right? is it because it fits the normal better or is there a better interpretation?

>>16447644
nm this is included in the [math]n![/math] term, now I'm curious too

>>16447660
Yeah the right fits better because the left's left side is all out of whack. I'm not sure why you're mentioning the normal distribution.

>>16447697
If you look at the bar graphs there is a normal distribution overlayed on it

>>16447759
no, those are Weibull and Gamma distributions, respectively.

>>16447759
A normal distribution is symmetric around the mean.

>>16447764
.... why am I retarded

Kind of a weird question. But I know phone cameras can pick up near infrared light. So when I pointed my phone camera outside from a window I noticed it was picking up a bluish purple light that i couldnt see with the naked eye. I noticed it was only picking up the light through the glass double pane window. I'm not able to see the light through window screen. I know there is a little bit of argon gas in the double pane windows, is that gas cause some visible light source to shift towards near ir?

Last thing There are no blue lamps near me

>>16448047
Tricky question to answer. It would depend on the sensor in your phone, the exactly frequency sensitivity of the device is unlikely to be public information. Not all double pane windows use argon, and even if it has it's not going to glow like a neon lamp. That requires electricity. Rayleigh scattering might be what is happening - enhancing blue+purple would be exactly this - but maybe more likely is the fact the camera is better at picking up low light than your eye and / or it's a post-processing image artifact.

>>16448145
Oh you know what. I just realized my camera has a laser auto focus so that was the laser reflecting back into the camera lmao.

>>16448165
Ahh, even if that's not what you originally thought it's still kind of cool.

>>16448180
nice try cia, why are you trying to cover up secret argon resonators hidden in everyday windows? What's up with that?

Allegedly there is a structure (organellum?) in human cells whose purpose remains completely unknown (assuming it has any purpose.) Is that true?

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Let [math]J^k(V)[/math] be the subspace of [math]\bigotimes^kV[/math] spanned by all tensor products [math]\bigotimes_jv_j[/math] such that for at least two different indices [math]j,l[/math] we have [math]v_j=v_l[/math].
How can I prove that [math]J^k(V) = S^k(V)[/math] where [math]S^k(V)[/math] is the subspace of symmetric tensors?
I need to do this because I want to use the first isomorphism theorem to prove that [math]\bigotimes^kV/J^k(V) \cong A^k(V)[/math] where A is the subspace of skew-symmetric tensors.
I defined a map [math]\varphi : \bigotimes^kV \to A^k(V)[/math] that takes any tensor and spits out its skew-symmetric part, since any tensor can be uniquely written as the sum of a symmetric and a skew-symmetric tensor. So I just gotta prove that [math]\ker(\varphi) = J^k(V)[/math].
Refer to pic related.

I'm trying to obtain the action angle variables for a central force
problem. How do I integrate this thing?
[math]f(x) = \int_{a_{min}}^{a_{max}} \sqrt{E+\frac{1}{x}-\frac{1}{2x^2}} dx[/math]
I know you're supposed to get something similar to this
[math]f(x) = - 1 + \sqrt{-\frac{1}{2E}} [/math]
but most books just say
>trust me bro

>>16449472
I do not know where you got that integral from because it does not give a result anything close to what you seem to be expecting.

>>16449472
I'm gonna swap your notation f(x), a_max, a_min for I, b, a, respectively
[eqn]I= \sqrt{-E}\int_a^b x^{-1}(x-a)^{1/2}(b-x)^{1/2}dx [/eqn]
This looks like a hypergeometric function:
https://dlmf.nist.gov/15.6
So let's rescale the limits of the integral to be 0 and 1 to put it in a standard form.
[eqn] I = \sqrt{-E}\frac{(b-a)^2}{a}\Gamma(3/2)^2 \,F(1,3/2;3;1-b/a ) [/eqn]
Now Gamma(3/2)^2=\pi / 4, and you can simplify the hypergeometric function to an ordinary function using 15.9.17 of
https://dlmf.nist.gov/15.9

>>16449568
Yeah I worked it out to the end. You get
[math] I= \frac{\pi}{\sqrt{2}}\left(-1+\sqrt{-\frac{1}{2E}}\right) [/math]
There's probably an easier way, but this works

>>16449636
>>16449568
Thank you. Seems I had to use complex variable theory in the end

Suicide suicide suicide

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Explain why this wouldn't work

>>16450212
what do you mean? it would work

>>16450212
the ball needs to have significantly more momentum than the bear, but it would work

>>16450212
The ball would need to bounce pretty well and be pretty heavy. And the bear would have to be very good at aiming to keep hitting it. But apart from that it seems like it should work.

>>16450212
Coming soon to an anime near you.

I don't understand what they mean by this. Do they perhaps mean this action [eqn]\mathbb{Z} \times \mathbb{S}^1 \to \mathbb{S}^1, \quad \quad \left(k,\, e^{2\pi i\, \cdot\, \alpha}\right) \mapsto e^{2\pi i\, \cdot\, (k\, +\,\alpha)}.[/eqn]

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>>16450550
Forgot the picture.

>>16450552
[math]\mathbb{Z} \times \mathbb{S}^1 \to \mathbb{S}^1, \quad \quad \left(k,\, z\right) \mapsto e^{2\pi ik \alpha}\cdot z
[/math]

>>16450909
thank you

>>16436512
What happened to /our/ guy's channel, Norman Wildberger? His videos are all gone. Set theorist jews conspired and got him... Our hero is down.

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Each line has different spacing somewhere. Which one looks best?

>>16451023
They all look the same. Stop being so schizophrenic about millimetric spacing on your equations.

>>16451023
The third one is correct and would be automatically set if you had actually bothered to use \cos{\phi} and not cos\phi

>>16451092
>\cos{\phi} and not cos\phi
These yield the same spacings

>>16450984
It says he removed them himself.
That's upsetting. I liked his stuff.

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Wait WTF, so nuclei can indeed have protons that orbit around other neutrons/protons and nuclei aren't always round and can look like fucking rice grains? HOW? All my physics teachers lied to me. My whole life is a lie.

>>16451151
Nuclear physics is complicated and all models are an approximation. Also those configurations are inherently unstable and decay within milliseconds.

>>16450212
The other answers are wrong. Momentum is a vector quantity. The momentum of the bear must be to the right at all times. But the ball is the only source of the bear's momentum. This means the ball would have to be moving to the left. But the bear can only reach the ball when it's moving to the right.

This means that the only way the bear can get across is if he does this in only one step. This is the same as a rocket problem; you can only move forwards when something else is pushed behind, so you can't just throw a ball backwards and try to catch it, cause you'll just end up at the same initial spot. Notice that this is just Newton's 3rd law

>>16451186
to the right relative to the bear, btw

>>16451186
False. Yes, the bear transfers momentum down and to the left, but if the ball already has a strong up/right momentum the energy loss will be trivial enough to get him across.

>>16451218
What has energy got to do with conservation of momentum? Pushing the much heavier bear to the right will have a greatly increased change in velocity of the ball to the left. And if the velocities don't match, how are they meant to stay in sync??

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I don't get why this guy (Steven H Simon in Solid State Physics chapter 15) acts like k is periodic for a free electron perturbed by a periodic potential. Since there still is an electron with [math] E_0 = \frac{(k \cdot \hbar)^2}{2 m} [/math], shouldn't the energy for [math] k = 3\pi/a [/math] always be bigger than for [math] k = pi/a [/math]?

>>16451340
A free electron has energy [math]E \propto k^2[/math] but inside the band that is instead something like [math]E \propto \cos{ka}[/math]. This is a fairly standard result in an quantum system with boundaries (the gaps). It might be covered later in the book.

>>16451242
>Pushing the much heavier bear
This is where your claim falls apart

>>16451866
You sound like the type of person that has sex with incels

>>16452289
Lol just ignore him

>>16452332
Fag
>>16452289
Fag
>>16451866
Fag

why do magnets attract each other if they have zero relative velocity

>>16452625
never mind i read that it's because of particle spin

>>16452625
That is what attraction or any other force does. It causes a change in velocity.

>>16452636
but the magnetc force is the cross product of velocity and the field, so it needs to be moving?

>>16452640
You are talking about the classical EM force. You are right that the magnetic field of magnets is due to spin, and that is a quantum mechanical effect.

How to measure the volume of a fluid from a spray nozzle
I'm using minoxidil and it came with a spray nozzle and a dropper. I want to use the spray nozzle because it's more sterile I guess but nowhere on the packaging is it mentioned how much one spray is. Is there any way of calculating it, I don't have the tools to measure accurately. I'm guessing it would be something like pipe area*swept length right?
Supposed to use 1ml twice a day

>>16452932
Fill the spray with water. Do full sprays for N reps, and M sets. You can calculate the water loss by weight loss (prob not accurate) or by volume (maybe little more time consuming depending if you're collecting the water or measuring what's left). Find the average loss per spray.

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>>16436512
I flunked maths in high school and I feel like I’m mathematically illiterate (aka I’m retarded). How can I improve my maths skills at home / as a hobby? Are there any specific types of maths I should focus on learning (besides add/sub/multi/divide)? Any websites I should check out?

>>16452996
I figured doing that but again I want it to be sterile
Then again, 95% of the solution is isopropyl alcohol so it really wouldn't matter since that's antibacterial right?
>>16453002
Look up knot theory. I suppose it would be the easiest math field where a layperson could make actual advancements

/sci/ is probably not the right board for this but here goes
What's that psychological bias where every piece of evidence is used as confirmation of ones beliefs
I remember this clip used to illustrate where something was happening was used as evidence for both X and not X by two different people

>>16453164
confirmation bias

>>16453164
Confirmation bias, social media algorithms thrive on it.

What is the amplitude of a photon? Can it be predicted? How many nanometers wide are they?

>>16453295
Photons do not have an amplitude, they are not that kind of classical wave. As for their width or size, that depends on what precisely you mean. Since a photon is an excitation in the quantum electromagnetic field they do not a physical size. However you can talk about what affect they have on their surroundings and calculate something like their cross section in scattering processes. That result would be related to the wavelength of the photon.

Does anyone have that reddit post from a teacher telling how bad his students are as they fail to comprehend and apply basic concepts and even do basic tasks?

Does anyone have a link to the proof that two differentiable structure on [math]\mathbb{R}[/math] are necessarily diffeomorphic.

I'm not a math guy so there's prob details missing. Idk but here's what I feel is the gist of it:

If f(x) = x^2 and f(c) = 4, you can't tell if c = 2 or -2. If you're working with homeomorphic functions, it should work then. Notice that this fucks up where f'(x) = 0, cause that's when the curve goes back up (or down) and retraces over the same values of f(x).

Given f(x) and g(x), the diffeomorphic map between the two is the continuous function (f o g^{-1}) and inverse (g o f^{-1}), and not past f'(x) = 0 or g'(x) = 0. So for something like f(x) = x^3 and g(x) = x^5, the first map works for p \in (0,\infty). Something like p = 32 you can put into g^{-1} to get 2 and you can cube it to get 8. So 32 maps 8, and the differentiable function that maps it is p^{3/5}. Diffeomorphism just means (f o g^{-1}) and it's inverse are differentiable and a bijection. You can just do chain rule on (f o g^{-1}) and inverse (g o f^{-1}). Composition of homeomorphic functions are homeomorphic, so it's a bijection.

>misc
The use of the jacobian when talking about diffeomorphisms is because this means that when it's determinant is non-zero at some points, the inverse function exists around those. The way to show that it's a diffeomorphism is to use the Inverse Function Theorem (IFT), which shows that the inverse map for a differentiable function is differentiable around those points (so locally). For one dimension the Jacobian is just the derivative, which you can use chain rule on (f o g^{-1}).
We intentionally chose the domain to exclude when the derivatives of f and g equal 0, which means (f o g^{-1}) won't be zero either. The IFT then guarantees the existence of the differentiable inverse function we want.

You can prob look up details on google, like How to prove the IFT, or the proof of composition of homeomorphic/cont. functions are homeo/cont too, or why nonzero jacobian determinant (the inverse of the jacobian matrix exists) implies an inverse func, wtv you really want.

>>16453444
oh woops, somehow the @ was missing in >>16453737

>>16453309
>Since a photon is an excitation in the quantum electromagnetic field they do not a physical size.
That doesn't make sense. Why wouldn't they?

>>16453751
All fundamental particles are point-like. Their 'size' comes about from how we measure them.

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>>16453758
>All fundamental particles are point-like.
How do you distinguish between an electron and a black hole of the same mass and charge, then?.

>>16453762
You wouldn't have to. A black-hole that small would instantly evaporate due to Hawking radiation.

find all [math]z \in \mathbb{C}[/math] such that [math]z^4=\overline{z}[/math] . Can someone solve this?

>>16453804
Convert to polar coordinates, z = Re^(i*theta). Or ask Chatgpt for hw help. Remember that theta + 2pi*n == theta to get the general solution

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>>16453804
>find all [math]z \in \mathbb{C}[/math] such that [math]z^4=\overline{z}[/math] . Can someone solve this?
WolframAlpha can https://www.wolframalpha.com/input?i=z%5E4%3Dconjugate+%28z%29

warosu.org is down, can anyone remind me what the other /sci/ archive is?
I don't mean archived.moe, it was something that also archives /3/, if I remember correctly.

>>16453943
Fuck me it's literally in the OP. I don't remember seeing it there in the past, my bad.

>>16453864
analytically how am i supposed to reach the solution without using polar coordinates?>>16453842

>>16453949
first look at the modulus, taking a complex number to some power takes the modulus to the power as well and taking the complex conjugate does not change the modulus so we have [math]|z|^4=|z|[/math], so the modulus is 1
next use the fact that [math]z\cdot\overline{z}=|z|[/math] and substituting that in you get [math]z^4=\frac{|z|}{z}=\frac1z[/math] or [math]z^5=1[/math]

>>16453963
>so the modulus is 1
Ahem, modulus is 1 or 0.
>>16453949
Substitute z = a + b*i, expand left side, get real and imaginary parts of resulting equation, have fun solving system of equations of fourth degree for a few hours.

>>16453758
>All fundamental particles are point-like.
NTA but how exactly do we know this?

>>16454056
Because that is what quantum field theory tells us, that every fundamental particle is an excitation in their associated field and has zero volume.

Why is the human brain so slow at math? I guess at language too now that AI is a thing. AI might not get facts right but it has good grammar. Calculators solve problems faster than anyone but they dont know what the problem is.

>>16454253
General vs Specialised. A calculator is built to do only math and do it fast. The brain is built to do anything, including building a calculator or an AI.

>cant seem to force myself to want to do what it takes to succeed in school
>no other obvious avenues in life
how did you do it /sci/fags? ive failed core classes in my cs degree path several times now, and every single day i tell myself i will do things differently, and then i just regress and continue to do the same shit day after day. i haven't been able to convince myself that any of this shit matters. i sit down for a couple hours, struggling with my coursework only to get so frustrated with being completely unable to learn what im supposed to, and start making mistakes and losing points, or i'll do great on homework assignments for an entire chapter, then bomb a test because it turns out i don't actually know how to do the problems, i only know how to look up textbook examples or watch youtube lessons. it's like learning a language with a pocket dictionary in your hand at all time or something. i simply can't grasp this shit at the rate im expected to and i have poor retention

it just kills whatever motivation i have, and all of this is coupled with a constant deluge of horror stories i hear from STEM industries of graduates not being able to find employment with their degree. let's say i did put my shit together and graduate. i wouldn't have anything higher than a 3.0, guaranteed. i have virtually zero chance of finding employment anywhere.

>>16454535
lord have mercy, i promise you anon, you will get a job with a CS degree.
what classes have you had success in? what did you do differently in those?

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Any Medfags out there?

What blood type am I?
I do not understand how to read this secret medical code.

Pretty sure it says I'm type A (child)
But I specifically wanted to know if I'm Rh negative or positive.

Also anything else you can decode from this medical gibberish is appreciated.

>>16454561
>>>/sci/med/

>>16454561
It's the line labled Rh.
D = D antigen gets produced
d = D antigen does not get produced
C = C antigen gets produced
and so on...

>>16454561
> But I specifically wanted to know if I'm Rh negative or positive.
Having the Rh D antigen (which you do) make you Rh positive (+), without the D antigen you would be negative.

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>>16454581

I slightly came to that conclusion earlier in a Google search but I was not positive that I was correct in my assumption. Thank you anon.
A quick google search does not really quickly get you a black and white definition of what they are explaining here.

/x/fag here.

I wanted to know because a majority of supposed alien abductees are RH Positive. Supposedly.

Thanks /Sci/ my business with you here is done for now. I'll be back. Biology nerd here. I bet you guys hate on us for some gay 4chan hater reason. I like trees,cells and soil science fuck you math nerds.

d fug happn'd?

https://imgur.com/gallery/fuuuuuuuuuucccckkk-Q3U7xFs

>>16454592
>/x/fag here.
Are you stupid?
>I wanted to know because a majority of supposed alien abductees are RH Positive. Supposedly.
IIRC 85% of Homo sapiens is Rh+.

if a=o(r^n-1) where r=sqrt(h_1^2+h_2^2+...+h_m^2), how is it that a* h_i=o(r^n)?

>>16454677
Yes. Yes I am. Stupid that is. That's why I've frequented 4chan since 2007.

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Help on, t-desgin + graph, can someone enlight me, I do not get it.

> How do you generate a non-infinity block
> Are there more than one block containing infinty

I tired everything, and manage to obtain blocks of size 6... but I think it's wrong, to do so I have removed all edges incident to the vertices forming the edge to encode, it gives me 6 edges but it is not two distinct triangles. I'm kinda lost.

>>16454698
You might want to give a bit more context than a dry ass equality with n numbers we know nothing about

>>16454698
what is o? big O?

>>16455379
Probably small o.

>>16455078
Where is the problem? Label the vertices 1,2,3,4,5,6. The pairs of two triangles are
123 + 456
124 + 356
125 + 346
126 + 345
134 + 256
135 + 246
136 + 245
145 + 236
146 + 235
156 + 234
All those blocks contain 6 edges. Three from each triangle. Then you have 6 other blocks with the claws and points of infinity for a total of 16 blocks just as needed.

>>16454673
someone mined a sand block and the gravity physics kicked in.

>>16454673
Probably a cavern collapse

Find two numbers x >= 1 and y >= 1 such that xy = 50 and 2x + y is a maximum.

>>16456345
Am I missing anything or is this simply (x, y) = (50, 1)?

>>16456355
Ok but why? How did you get the answer?

Why do men smell worse than women?

>>16456357
By guessing, I guess? You look for maximum of 2x+y so you want x to be as large as possible. Given the conditions (xy = 50 and y>=1) the largest possible x is 50. (It's midnight. No idea if it makes any sense.)

Find the dimensions of a right triangle of maximum area whose hypotenuse has a length one.

>>16456413
I got it, its width and height equal [math]\sqrt{1/2}[/math]

Why doesn't blackbody radiation go green? It goes from red to white to blue, but never green for some reason

>>16456748
The frequency range the human visual system sees as pure green in incredibly narrow and when black body radiation peak is within that range (~6000K) there is still enough blue and red light being produced that our brain ends up seeing white instead.