Mathematics - 2017-08-03 (page 1 of 4)

Ted Shifrin

00:02

hi mr @Pedro :)

Daminark

Hey @Ted!

Ted Shifrin

00:21

hi Demonark

Akiva Weinberger

@SimplyBeautifulArt The cup is twice as large as it needs to be

Simply Beautiful Art

@AkivaWeinberger Can I call that a conservative statement?

Ted Shifrin

heya DogAteMy, SBA.

Jasper Loy

My answer appeared on the queue for low quality answers and I was rebuked by a reviewer, lol.

Oh well, I think the algorithm for determining such posts is quite bad and might as well be done away with.

Ted Shifrin

Way to go, Jasper!

Link to it and let me be the judge.

Jasper Loy

00:31

It's nothing to judge, just a silly thing, lol, so I won't bother. =)

How is the semi unretirement?

Ted Shifrin

Then don't bother bitching about it?

Jasper Loy

I guess you are still teaching some classes?

Oh OK then, no more bitching. =)

Ted Shifrin

I'm going to teach one high school class at a super-math high school which is enrichment for the kiddies.

Jasper Loy

What is supermath? LOL

Ted Shifrin

But it's all a universal curriculum, with universal lesson plans, homework, tests, etc. I've never quite taught in such a situation, but I'm looking forward to being in the classroom.

Jasper Loy

00:32

It must be mathoverflowoverflow, lol.

Ted Shifrin

It's Art of Problem Solving. Mostly on-line students all over. Google it.

But they have a few actual schools, and they're opening a new one in San Diego in a month.

Simply Beautiful Art

Hey Ted

Jasper Loy

Ah, OK. But the term supermath sounds a little pretentious, which sounds like your favourite word obnoxious.

Simply Beautiful Art

Oh right! AOPS!

Ted Shifrin

Well, they teach essentially only math. That's what I was referring to.

Jasper Loy

00:33

In fact, earlier today I used the word obnoxious in the other chat room.

Simply Beautiful Art

If anyone has experience with AOPS and would like to answer this meta question, please do.

Jasper Loy

I learnt the word from you, lol.

Ted Shifrin

It's a common English word :)

Tobi

Im building a game and am trying to figure out how to distribute velocities between two circular objects

Ted Shifrin

SBA, what does that post have to do with AoPS?

Tobi

00:35

from my physics lessons, i know you can use the momentum equation, mu+mu = mv+mv

Ted Shifrin

@Tobi: You want to conserve momentum, energy, and angular momentum, assuming no inelastic collisions occur (and there are no external forces/torques).

Akiva Weinberger

@JasperLoy What's your native language?

Jasper Loy

@TedShifrin Wow, I didn't know your physics is so good, lol.

Tobi

looooooooooool

Jasper Loy

@AkivaWeinberger English and Chinese.

Tobi

00:36

mv^2 = mu^2 right

Ted Shifrin

I had a fabulous freshman physics course in college, Jasper. And I love that stuff.

Different m's, @Tobi? And remember that velocities are vectors.

Jasper Loy

I did take a few physics courses in college but I have forgotten everything including Newton's Laws, lol.

Tobi

I still remember the laws

Ted Shifrin

In my multivariable math course I did several lectures that were mostly physics.

Tobi

So, conserve energy and momentum?

at the moment im only conserving momentum

The initially moving object stops, and the still object then moves at a proportionate velocity

Jasper Loy

00:38

I am trying to conserve money, lol.

Tobi

and it breaks down when theyre both moviing

Theres a constant deceleration for all objects on the surface

I did calculation and everything cancelled out

to Mu = acceleration

where mu is coefficient of friction

Ted Shifrin

That's a standard collision problem, Tobi. Use conservation of both momentum and energy.

Tobi

but it doesnt take into account velocity

Ted Shifrin

coefficient of friction where? ... then no conservation of energy

Tobi

yeah the math is completely off

Ted Shifrin

00:40

pages @Semiclassic

Tobi

heres what it looks like at the moment

One component of velocity gets to 0 before the other

so it looks weird

it goes from diagonal to vertical/horizontal

Ted Shifrin

So usually the collision won't make one stop. Have you figured out when that happens?

Tobi

instead of decelerating each component seperately, should I turn the velocities into one (pythagorus) and decelerate that?

Ted Shifrin

I think you should first solve this with no friction.

Tobi

i remember there are different types of collisions from my physics course

Semiclassical

00:43

collisions are tricky to model if memory serves.

Tobi

depending on the relative weights

Ted Shifrin

Hey you. Thanks for responding to the page :)

Semiclassical

lol

Tobi

theres the collision where they stick together and move as one

theres the one where a smaller object rebounds

Semiclassical

yeah, elastic vs. inelastic.

Tobi

00:44

and where it loses all and the other gains all

Jasper Loy

@Semiclassical Especially boy-girl collisions.

Tobi

imagine i didnt take physics

id be so lost

Ted Shifrin

Imagine you also knew no math. Why would you be doing such a project?

Tobi

to make money

joke to consolidate knowledge

Semiclassical

more generally there's the so-called coefficient of restitution. if it equals 1, same kinetic energy goes in as comes out.

Tobi

00:45

building a mini graphics library

yeah im using coefficient of friction

Jasper Loy

@Tobi Then you should join the game Wheel of Fortune.

Tobi

prob the same thing, but different name over there

its from 0-1 as my teacher said

Ted Shifrin

No, those are different things, Tobi. Go read.

Tobi

oh ok

Semiclassical

yeah, coefficient of restitution is different.

I would definitely suggest doing as Ted said re: doing this without friction first.

Simply Beautiful Art

00:47

@JasperLoy Wow, that's still a thing? I wonder how long its been going

Tobi

they would bob infinitely

Jasper Loy

@SimplyBeautifulArt I don't know. The last time I watched it was years ago, lol.

Ted Shifrin

Um, no, Tobi.

Tobi

the friction is the only thing slowing them down

Daminark

How's it going everybody?

Eric Silva

00:49

Hi chat

Tobi

for the same material, is the frictional deceleration constant?

Eric Silva

@Daminark it seems we enter at the same time

Daminark

Yeah, weird

Jasper Loy

@EricSilva Maybe the two of you are one, lol.

Tobi

Fr = mu* m* g = m * a => a = mu * g => a proportional to mu

Ted Shifrin

00:50

Tobi: If two you have two balls of identical mass and no friction, when the collision occurs, if it's elastic, one will stop and the other will move.

Eric and Demonark are definitely hanging around too much.

Daminark

Ah crap Jasper is on to m... To u... Wait hold on no what are you talking about?

Eric Silva

Yeah I've been on here way too much lately

Jasper Loy

They are talking about momentum.

Ted Shifrin

@Jasper: They definitely look very different and have totally different mathematical taste.

Daminark

@Ted it seems like at any given time I'm doing something very excessively, I started getting on here right after my Undertale craze began to subside

Ted Shifrin

00:51

You're just tired of my asking if you've solved the geometry problems, @EricSilva :P

Tobi

I looked at the restitution thingy, so its the ratio of relative velocity before and after collision???

Eric Silva

I couldn't be doing work RN even if I wanted to

Jasper Loy

@TedShifrin Talking about taste, I am trying to be vegetarian now.

Simply Beautiful Art

@Tobi According to momentum, you should be able to get V's in terms of t's, and using a = dV/dt, get a differential equation.

Eric Silva

So I feel no guilt

Ted Shifrin

00:51

I'll never do that, Jasper. But my sister is vegan.

Eric Silva

@Ted probably

Tobi

whats the standard way to distribute the velocities of the discs, in 2 dimensions?

Ted Shifrin

Simply: You don't need no stinkin' differential equations.

Eric Silva

I've made a lot of headway trying to decipher Bryant lately though!

Jasper Loy

@TedShifrin Ah, I know of some people who are vegans. But vegetarianism is a good first step towards veganism =)

Eric Silva

00:52

So at least there's that

Semiclassical

@tobi that's problematic, if memory serves.

Ted Shifrin

OH cool, Eric. I haven't even looked cuz you haven't warned me.

Daminark

Also @Eric was dynamics a train wreck today?

Eric Silva

I wasn't there @Daminark

Ted Shifrin

@Jasper: I have no desire to do either, but I'm not gluttonous re meat (unlike most Americans, who also kill themselves with unhealthful prepared foods).

Semiclassical

00:53

if it's an elastic collision, then it depends on where the two disks collide.

Ted Shifrin

Demonark, you're not supposed to be skipping classes.

Eric Silva

I was in Logan square cause I had a reservation at a really nice macanese restaurant

Jasper Loy

@TedShifrin Yes, Americans are like one of the fattest people on earth lol

Daminark

Schlag gave me permission to leave due to this RTG

Ted Shifrin

NO arguments from me, Jasper.

Daminark

00:54

I'm in Indiana right now

Ted Shifrin

ohhh ... are you at ND now, Demonark?

Semiclassical

if one in motion hits another identical one at rest head on, then one will come to rest and the other one one will be left moving (b/c hey that's basically a 1D collision)

Ted Shifrin

Ah, cool.

Eric Silva

Ah yeah the topology thing

Ted Shifrin

Say hi to my friends at ND, Demonark.

Daminark

00:54

I am, it's been pretty fun

Tobi

if its elastic, does one always stop?

Daminark

Who are your friends?

Simply Beautiful Art

@Tobi No

Tobi

cries

Simply Beautiful Art

Are they both moving before the collision?

Semiclassical

00:55

if it's head on, with one at rest initially and both identical, yes.

but that's the exception, alas.

Tobi

if its elastic, can I use m1u1+m2u2=m1v2+m2v2?

Semiclassical

sure, if you realize that those u's and v's are vectors.

Tobi

im currently storing my velocities in vector form

but how do i know the final velocities, if i was given one final velocity, i could find the other

Eric Silva

@Ted I'll basically be ready to talk about Bryant after this weekend

Semiclassical

eh, if you've got an elastic collision, then you've got another condition (energy conservation) as well.

Tobi

00:57

angle?

Ted Shifrin

Demonark, Nancy Stanton (complex geometry) I've known since my freshman year in college. She knows me well. The others I know seem to have disappeared. Larry Taylor (topology) probably won't remember me. Brian Smyth might remember me. Andy Putman I know via friends on FB, but we've never met.

Whoa, OK, Eric. Which sections should I look at carefully?

Semiclassic: I mentioned that first thing.

Eric Silva

I'll tell you when I have it in front of me, I'm in the car atm

Ted Shifrin

I hope you're not chatting whilst driving.

Eric Silva

Oh no I'm in a taxi

Semiclassical

here's a good app for all of this @tobi

phet.colorado.edu/sims/collision-lab/collision-lab_en.html

Ted Shifrin

00:58

Who takes taxis these days?

Daminark

Eric does

Ted Shifrin

What was that, @PVAL?

Eric Silva

I would never drive in Chicago tbh

Ted Shifrin

I've driven in Chicago.

Tobi

how do they calculate it?

PVAL-inactive

00:59

Tobi

these are only head on

Eric Silva

It was raining pretty hard so I took the first thing I was presented with

Ted Shifrin

LOL ... I was never so rich in grad school. I walked in the rain.

Eric Silva

I don't like driving in big cities

Ted Shifrin

Don't try CA, then, Eric.

Semiclassical

00:59

@tobi go to the Advanced tab

Eric Silva

Schlag is the source of my disposable income

Ted Shifrin

Figures, given the name :)

Schlag = cream

Eric Silva

I may not look at Bryant tonight though, I have to prep a gmt lecture for tomorrow on some hard Theorems

Tobi

this 2 complikate omgggg

Eric Silva

LOL

Ted Shifrin

01:00

Sure. Just let me know so I can do a few hours of homework.

Eric Silva

Mmk

Daminark

Oh I remember seeing this one thing about him

Semiclassical

17 mins ago, by Semiclassical

collisions are tricky to model if memory serves.

Tobi

omg @Semiclassical the advanced tab is exactly what i need

Simply Beautiful Art

A fun side-note, you can obtain some sort of value for that series at $x\ne0$ using the Gamma function:
$$\sum_{n=0}^\infty x^nn!=\int_0^\infty\sum_{n=0}^\infty x^nt^ne^{-t}~\mathrm dt = \int_0^\infty\frac{e^{-t}}{1-xt} = \frac{e^{-1/x}}x\operatorname{Ei}(1/x)$$
However, the funny thing is that this is by no means an analytic continuation... so what is it?

PVAL-inactive

01:01

@Ted I I needed to post a picture as a comment. So I posted it here and linked it.

Ted Shifrin

Demonark: You saw my list of names?

Semiclassical

yeah, they've got some really nice apps there.

Daminark

google.com/url?sa=t&source=web&rct=j&url=http://…

PVAL-inactive

The picture is supposed to show the answer to this question math.stackexchange.com/questions/2380035/… doesn't work.

Ted Shifrin

Kaffee mit Schlag, aber natürlich

Simply Beautiful Art

01:02

Assuming the integral and summation change is necessary to make any sense of that sum.

Daminark

Yeah I saw, I'll try to find people tomorrow after the talks

Ted Shifrin

cool, Demonark. Nancy will freak out if you find her. :)

She's a bit stiff at first but really a nice person.

I haven't seen her in decades and decades.

This is summer, so probably most people won't be around.

Daminark

I will say that Andy Putman spoke today

A bit on covers, representations, and homology

Tobi

@Semiclassical what can I read to build the advanced tab

Semiclassical

I was just wondering that myself.

Eric Silva

01:06

@Ted I had this amazing skirt steak today, with some twice cooked plantains in a chimichurri sauce

Changed my life tbh

Ted Shifrin

LOL @changed my life.

Semiclassical

They may not have it online, tbh.

Ted Shifrin

I don't eat much beef, but I do love chimichurri.

Eric Silva

And probably the best Portuguese egg tarts I've had in my life

And I've had them in Portugal

Ted Shifrin

I don't know the Portuguese version, but I'm not a fan of those in general

Eric Silva

01:07

I love em but they're like a childhood snack

So lots of nostalgia there

Ted Shifrin

Yeah, I get it ... I don't much like flan or crème brulée either.

Semiclassical

@tobi This looks like a pretty good summary of 2D collision simulation stuff : gamedevelopment.tutsplus.com/tutorials/…

Tobi

jesus christ

i hate reading

Ted Shifrin

get over that!

Eric Silva

@Ted my mothers flan could win you over guaranteed

Bob

01:10

I recently tired to ask a question on StackOverFlow and it says that I need to login in to ask a question. I logined in and it says that I have asked too many bad questions so I cannot longer ask questions. It also says that I did not ask any questions. Any ideas?

Ted Shifrin

I'm dubious, Eric, but I'm open to the bribe.

Eric Silva

A friend of mine once drove four hours just to have some

In portuguese we call it Pudim

Topologicalife

Hi. Given any definite integral in $[a,b]$ if we make the subt $u = x(x-a-b)$ then we can prove all integrals are zero.

OO

Ted Shifrin

Eric, I had friends who drove several hours to have dinner at my house, so I don't buy that one :P

Yeah, @Topologicalife, but it's garbage.

Eric Silva

:P food is the great uniter I guess

Topologicalife

01:14

Or $\int_{-1}^1 x^2\mathrm{d}x$ into the subt $u = x^2$ :D

Ted Shifrin

puts @Topologicalife on ignore

Topologicalife

:D :D :D

Eric Silva

my mom also makes a mean mango mousse

to die for

Ted Shifrin

Now that I will die for.

Topologicalife

I just was explaining the 'horse paradox' to some friends.

I tried and tried but they didn't understand it. Now they believe all horses are red.

Ted Shifrin

01:15

All of mine are purple. Damn.

Isn't induction great?

Eric Silva

the mangoes produced on my moms tree are honestly magical

I've never had any that managed to match the flavor

Daminark

Oh yeah my calc prof used that to mess with us when we were first learning induction

Ted Shifrin

OK, I'm on my way. Tell me when/where to make reservations.

Eric Silva

ahahhaah

Daminark

Also he gave us this one paradox which messed me up

Like, you have a right triangle

Side lengths 1,1, root 2

Ted Shifrin

01:17

"Like"?

Topologicalife

Or I can be rich: $$1$ = 100c= (10c)2= (0.1$)2= 0.01$= 1c$$

Daminark

But if you try to approach the hypotenuse via stairs, you'd get a length of 2

Ted Shifrin

Oh, right. That's the standard thing people don't understand about integrals.

In engineering notation, $ds\ne dx$.

Eric Silva

isn't that because the convergence isn't in $C^{1}$

the length functional isn't continuous in $C^{0}$

Ted Shifrin

It's not even Lipschitz.

Right, uniform convergence doesn't solve everything. Curvature is worse.

Daminark

01:21

Yeah that's the issue, as it turns out

Twink

don't wanna forget how it feels without lithium...

Eric Silva

it's the same as the $\pi = 4$ thing

Ted Shifrin

Students standardly are bothered by the difference between volume integrals and surface integrals. But this is the key issue, Demonark.

Yikes, @Twink.

Twink

what? :(

Ted Shifrin

Lithium scares me :)

Twink

01:23

me too

I don't lilke it

Eric Silva

I guess one could do a $\pi = n$ paradox the same way

after reading some GMT a lot of the things Andre told me back in the Willmore course are starting to make much more sense

Twink

I want to stay in love with my sorrow

Semiclassical

@Twink Pretty much the perfect song for that: youtube.com/watch?v=D6p_qe45miY

Secret

[Chemistry]
ok, so I am going to code a modified gram schmidt to rotate the rotational axis of my 3x3 rotational matrix so it points to the correct direction. Now to learn some python...

Daminark

@Balarka so I've connected an external keyboard long enough to log in, and now I've pulled up an onscreen one

gian

01:45

Can someone answer a question of mine from Munkres?

Tobi

KE1initial + KE2initial = KE1final + KE2final

KE = mv^2/2

can I do simultaneous equationiningism

for horizontal and vertical

gian

Equationingism?

Tobi

The two balls exert and equal and opposite force on eachother, right? how do i calc that

Lucas Henrique

$\frac{a^2 + b^2 + 1}{ab} = k \in \Bbb Z \implies k = 3$

(yo guys)

gian

Force is different than energy. You put the conservation of energy law...

Lucas Henrique

01:52

does anyone have an idea on this one?

Tobi

let me draw it

Everyone join me, awwapp.com/b/uquc67ben

lmfaoo

gian

@LucasHenrique, are $a$ and $b$ integers?

@Tobi, I joined.

Lucas Henrique

@gian yeah.

Tobi

is it just me or is that latex unformatted

Trevor Gunn

@Tobi Not just you, MathJax isn't enabled in chat.

gian

01:57

Click the link in the upper-right corner to learn how to render MathJax, @Tobi.

Tobi

awwapp.com/b/uquc67ben

whos trolling :/

who the fk keeps wipipng the board

Lucas Henrique

i was wiping it

since nobody told me I could not

sorry

Tobi

gian

Does it give you angles?

Tobi

I have the components of velocity, thus (initial) angles

gian

02:07

Okay so use conservation of momentum and preserve momentum for both components.

From there you get the velocity for both resultant components.

Tobi

yeah but how do I know the final momentums, if one stops, i can put all momentum into one of the ball. But one will not always stop, so i have 2 unknowns

gian

And then just use pythagorean theorem to get the final velocities.

You don't need the final momentums if the problem gives the angles after collision.

Tobi

m1u1 + m2u2 = m1v1 + m2v2, right?

gian

Right.

Tobi

oh i dont know after.

I konw the velocities before collision

the vertical and horizontal components

/ the resultant + angle

gian

02:10

Well you need to know the angles after collision to get final velocities.

Unless they give you some other information.

Tobi

Like?

gian

Well is it elastic?

Tobi

could i do simultaneous equation

with kinetic energy

and momentum

gian

Yes try that.

Tobi

would that take into account the angle at which they hit eachother

gian

02:13

Well if its an elastic collision then the kinetic energy is conserved.

And if you're given the masses and initial velocities, you should be able to solve a system of equations involving both conservation of energy and conservation of momentum.

Does that make sense?

Tobi

ill just assume it will

gian

Write out both conservation laws and plug in the info you're given and see what you're left with.

gian

02:28

@LucasHenrique, did you figure it out yet?

Tobi

02:47

gian

No raw data is given @Tobi?

Tobi

?

gian

Numbers.

Tobi

I have us, and ms, elastic collision

gian

What I'm asking is if they specifically tell you what the masses are. Like 5kg and 3 kg...

Tobi

02:49

yes

I have the initial velocities, and masses

gian

Give them to me.

Keshav Srinivasan

Can someone help me fix the Latex in my answer here:

0

A: Is there an epsilon-delta definition of the second derivative?

I basically cheated. We say that $f''(a) = L$ if $\forall\epsilon>0\exists\delta>0\forall h\in\left(0,\delta\right)\exists L_1,L_2>0:\left(\forall\epsilon_1>0\exists\delta_1>0\forall h_1\in\left(0,\delta_1\right):f\left(a+h_1\right)\in\left(f\left(a\right)+ \left(L_1-\epsilon_1\right) h_1,f\left...

Tobi

why do u need

I need to know the method to calculate final velocities

gian

Okay well it looks like you've got it.

To find the final velocities, plug in the data you have first. Then rearrange this result so that one of the velocities is in terms of the other.

Tobi

the equations have the final velocities, which I dont know

ive gotten to this

M1 * ( U1^2 - V1^2 ) = M2 * (U1 - V1) * (V2+U2)

is that correct?

after all of this time, all i needed was this: khanacademy.org/science/physics/linear-momentum/…

.......................

gian

03:07

Your problem requires doing it twice; once for each component. The video shows a one-dimensional collision if I'm not mistaken.

Tobi

its the same thing (procedure), yes twice, for each component

The Pointer

Can anyone please help math.stackexchange.com/questions/2379619/…

I've posted the problem and solution

Tobi

03:58

GUYS

I DID IT OMGGGGGGGGG

@Semiclassical

Semiclassical

nice

Tobi

Its not taking into account the angle of impact, though

because i think the formula are for point impacts

Semiclassical

yeah, I can believe it gets complicated fast.

The Raiders of Las Vegas

What is that?

Tobi

i couldnt find anywhere teaching how to do that

so i just did the physics on paper and got the equation

Semiclassical

04:05

How many objects can you have on screen at once?

Tobi

i dont know, havent tried

ill do so now

Semiclassical

A fun one, just to watch, is to turn off friction, put a bunch of balls in there, and then give one of them a high velocity.

it'll scatter off one of the other balls, transfering momentum to it, and then that one will transfer it to another, and so forth. and bam, you've just made a gas. :P

Tobi

should I use the normal velocities

Semiclassical

could not tell you.

Tobi

for getting proper angles

by normal velocities, i meen the component that is normal to the point at with the circles faces collide

would that fix it

Balarka Sen

05:03

@Daminark whew!

The Raiders of Las Vegas

05:15

@Twink keep taking it until you regain control of your sorrows, my friend. It's for your own good.

user84215

I come again with a new idea. Let us construct a university in MSE. Like other universities it would have classes (chat rooms), stuffs (professors, directors, president, ...), research groups and etc. We would also have Bachelor and PhD programs in it and give graduated students Bachelor and PhD degrees. Please go to MSE University for more details and sharing your opinions (please first read it completely and then say your opinions).

2

Jasper Loy

05:41

@aminliverpool I have read the details and I think the idea is doomed to failure, because SE just lacks individuals willing to give the time and energy for quality instruction. So much is needed just to conduct one single lesson, you know. Even if this university awards degrees nobody would recognise it. And there are already enough crap univerisites in real life, and this will be even worse.

The Raiders of Las Vegas

I'll have to agree with Jasper on this one; but it's a great idea in theory :-)

Jasper Loy

And seriously, I don't even trust SE in general for authoritative answers on any site. One can come here asking a question hoping that an expert will give an answer, but there is no guarantee the answer is correct or good, and there are so many high rep users on each SE site who know shit about the subject.

The Raiders of Las Vegas

Perhaps post it on meta. @aminliverpool

user84215

@JasperLoy Thanks for your comments and devoting your time to read my idea. First, you have said "SE just lacks individuals willing to give the time and energy for quality instruction", but I think it is not true because I have seen many MSE users with wonderful reputations (about 50 k and more). This fact indicates that many users spend many of their times and energy for math instruction and answering to people.
Second, you also have said "Even if this university awards degrees nobody would recognise it". I think that this degree would not be the main goal of all students to study math in …

user84215

@TheRaidersofLasVegas Thanks for your suggestion.

Jasper Loy

05:55

@aminliverpool Answering individual questions is not the same as conducting an entire course. If it is not an important goal of the students to get this degree, then this is just like a normal learning avenue, and there is no guarantee of the completeness or quality of the course.

Transcript for

$Mathematics$ Mathematics