Here you go! Those who are computer genius and have free time use algorithms to make it more heavenly!

I need to go out and observe light's property! Cee ya..

forbes.com/sites/jamiecartereurope/2020/05/21/…

The actual ANITAS result is very interesting, but once again the internet overblown it

today I dreamt of that I am on the way hurry to a law court to listen to a lawsuit.

You can get Civilization VI for free now.

I guess that will kill my productivity this weekend.

But I have to read three bids for a big project now. I guess I just throw a three-sided coin.

@WhyWhatWhereWhenHow xxxDD thanks for showing me this meme

@JingleBells My pleasure 🤳🏿.

I am so deep in memes that my physics knowledge is returning to it's primitive form.

@WhyWhatWhereWhenHow His head looks like $f\left(x\right)\ =\ -x^{2}$

@JingleBells Racist lol.

@WhyWhatWhereWhenHow ??? do you even know what racism is

@JingleBells showing or feeling discrimination or prejudice against people of other races, or believing that a particular race is superior to another.

You have bend to rule but not break it.

Saying that your head looks like an egg is not racism.

@JingleBells The limit of that comment approach racism but never touches it.

...

Where does this -2n come from?

And why is A = Z when as far as my logic goes 7a + 3b cannot be all possible integers?

(for example, what would a and b be so A = 1)

$A$ cannot be as integer but set of integer lol

yes my bad

hmm

I think I'll change the textbok

That Z is also set of integer lol

but wouldn't it be A = {{7a}, {3b} : a, b E {Z, Z}} then?

and we are choosing arbitrary integer as n

ahh nvm I'm confused af

and in this case we just randomly make n =7n+3(-2n)

we know 7a+3b is integer

and n is integer

but you said 7a + 3b is set of integers no?

@JingleBells dude 😂😂😂 it is integer but you know it will generate set of integer

and put in that set

My understanding is very messed up, I'll change my source of math info

Thanks for the help :-)

Book is good at explanation

But you have some flaw in set theory understanding

@WhyWhatWhereWhenHow not sure about that

@WhyWhatWhereWhenHow yes, I'm sure about that

@JingleBells It is goo at explanation. Very intutive for me at least since I already have good understanding of it

@WhyWhatWhereWhenHow I'm talking about the book's explanation of set theory, not the exercise example

math is fun never ceases to amaze me

@JingleBells Then I am not sure about your book. What's the name of that book?

It's probably true that I should not blame the book, but I think I can find better and more suitable math resources for me

@JingleBells are you a high schooler?

@WhyWhatWhereWhenHow yes

so you are slef studying aren't you

yes

Oh I need to go cya.... zap!⚡

cya

Ugh, Civ is free but it's on Epic.

Ah, back when the Simpsons were still funny

@ACuriousMind The Simpsons movie was 2007

Well past the "Simpsons are still funny" phase

Hm, I tend to forget I'm getting old :P

Aren't we all

This proves ACM is normal guy

I don't get old

I have a portrait in the attic who does it for me

can you recommend a painter for that?

I am so done with human conversation that I can nearly predict what human will say next.

@ACuriousMind I'm afraid you'll have to ask satan for that

Hi

time to draw the summoning circle, then

wow, that was fast

:DD

Suspiscious

Ok acm is not as normal as I thought :O

😲

Greetings @JohnRennie!

I thought the Simpsons movie was good, then again I haven't seen it since it released at which point I was 10 so who knows

My parents wouldn't let me watch it, that and the inbetweeners we used to quietly watch at my friends house, good times

I feel attacked!

...why?

@ACuriousMind what glitch you used to put crystal in your name?

I can't put crystal!

Oh I mean diamond

♦️

The diamond is a sign that the user is an elected moderator. It's not part of my username.

Is there any glitch so that I can put sticker in my name?

unlikely

I think You and Charlie are twin brother ....right?

Yes I am his distant cousin

AFuriousMind

lmao

Can the Maxwell relations be inverted? As in literally just flip the partial derivatives upside down and the relations hold?

as in thermodynamics not E&M

@Charlie Yes - because the inverse of a derivative is the derivative of the inverse.

Ah I see thank you

$$(\frac{dy}{d x})^{-1} = \frac{xp}{\lambda p}$$

seems legit

It is well known that derivatives have reflexion and discrete rotation symmetry

I already showed that the zero velocity curve is the parabola defined by $\mu x^2+y^2=\frac{1}{h^2}$, but now i need to show that in the case of negative energy (when $h<0$ in $E(X,V)=h$) the only solutions that meet the zero velocity curve and "are straight-line collision-ejection orbits for the system" lie on the $x$ and $y$ axes

I'm not sure how to get started on that, and I'd appreciate any hint

I think you might have used the wrong bracket on your \begin{matrix}

@Charlie i fixed it

I think after a certain period it doesn't let you alter messages, might have to repost it

\begin{align} x'' & = \frac{-\mu x}{(\mu x^2+y^2)^{3/2}}\\ y'' & = \frac{-y}{(\mu x^2+y^2)^{3/2}} \end{align}

I meant repost the matrix part, the part above was fine

@Charlie it's the same :)

ahhh my bad

@AlfredCentauri It's a mystery. Ben still has a few accounts on other sites, eg Astronomy but he's not very active.

@JingleBells The author knows how to solve stuff like that (& so did the Ancient Greeks. A guy named Diophantus wrote about it, and so did Euclid). But in the snippet you posted, it looks like he just pulled that -2n out of thin air. It works because 7×1 - 3×2 = 1. But there's a systematic way to find integer solutions (x, y) for equations of the form ax + by = c, and easy ways to tell if the equation has no integer solutions.

It's not really out of thin air. They're just writing $n = 7n - 6n = 7n + 3(-2n)$.

In terms of Diophantine equations, this would be phrased as $7a + 3b = n$ having integer solutions $(a,b)$ for every $n$. Which is true because 7 and 3 are prime and therefore in particular coprime.

But even without any knowledge of such equations in general, the author is just re-writing $n$ in the form $7a+3b$.

@ACuriousMind not for every n

isnt there a condition?

gcd(a,b) must divide n

Yes, and gcd(7,3) = 1.

Note that $a,b$ are here what's called $x,y$ in the Wiki article, and $7,3$ are what's called $a,b$ in the Wiki article.

oh yeah I misunderstood

apologies

no worries

Hi @FakeMod!

@ACuriousMind Sure. And that's pretty obvious to you & me. But we're familiar with linear Diophantine equations, and JingleBells isn't.

OTOH, I don't know the context of the snippet JingleBells posted. Maybe in the context of the textbook the solution to that 3a + 7b thing is more obvious to the careful reader...

The sign of the spring constant is to be chosen so that when compressing a string, the force goes in the other direction

Hi

@Slereah what about a spring connecting two masses. How do you deal with this one?

The same way

If the separation of the two springs is shorter than the one at rest, the force should be outward

What is the seperation?

@MadSpaces $|x_2 - x_1|$

@FakeMod If you think a question should definitely be closed but is bountied, flag it for mod attention. Moderators can refund bounties.

The website math is fun is currently the best source of math stuff I've found. Easy, simple, it has exercises

mathsisfun.com

xDDD

@FakeMod This is so funny!

@FakeMod Only 5 years late ;P

Where can I download RAM for Ubuntu xDDD