Mathematics - 2018-07-24 (page 1 of 2)

loch

00:00

@geocalc33 irrelevant but imo i think you might find it helpful to work through some basic textbooks in math (right now the impression you're giving is that you read about stuff from wikipedia and think of something that you think is cool - which if you're having fun with it is great but makes it rather hard for other people to communicate with you) - that way (a) people will more likely be able to understand what you're saying

and more importantly (b) you'll more likely be able to determine whether your questions are meaningful or not

2

Nick

!!answer proof of 1+1

why are there no bots in here?

Ted Shifrin

people are bad enough, Nick

I think there's a lurking Demonark, though

Daminark

00:31

Oh no, gotta watch out

Ted Shifrin

Yes, especially 'cuz it's shark week (or it just was)

Eric Silva

hello chat

Daminark

Yo Eric

Eric Silva

sup

Daminark

Not too much, you?

Eric Silva

00:37

too much

Daminark

Rip, bootcamp's heavy?

Eric Silva

the teaching has been not too stressful but the soug stuff has been

Ted Shifrin

@Eric !! Haven't seen you in weeks!

geocalc33

@loch working on it

Ted Shifrin

We're supposed to geometrize sometime.

geocalc33

00:40

@loch but at the same time i want to explore my own questions. I don't want to 1) learn math and then 2) explore math

Eric Silva

yes i am seriously feeling the lack of geometry :(

geocalc33

geometry?

here?

Ted Shifrin

See, Eric, you miss us :)

Eric Silva

honestly havent been into the math ive been made to do

Ted Shifrin

There's a moral in there somewhere, Eric.

But you might acquire a taste for it — you don't know.

Eric Silva

00:41

that is true

i can hope i might, to make this a bit more bearable anyway

loch

@geocalc33 that's understandable - but is also why not a lot of people respond to your questions lol - the analogy is you can't really do literature without knowing the alphabet well

but whatever floats your boat :)

Ted Shifrin

But, still, I'm willing to talk Bryant.

geocalc33

I'm willing to be mercilessly criticized

Ted Shifrin

The modern trend of having undergraduates do "research" when they barely know calculus is interesting, @loch, but this is a variant of that.

Eric Silva

hopefully ill find the time after i finish prepping this lecture im doing tmr

im so behind, i was extremely sick for a bit and it put me in a bad way

Ted Shifrin

00:43

I'm sorry, kiddo. Get better, and don't stress so much.

Eric Silva

ty

loch

@TedShifrin that's a thing?

Eric Silva

i will try not to

Ted Shifrin

@loch: It's been a thing for years now.

Daminark

Wait as in, trying to do original research? Do they just find some problems that are accessible and that nobody has time to do and just give them?

Ted Shifrin

00:45

Demonark, "undergraduate research" is the modern hot button. You guys have your own version of that, but at a higher level. Freshmen advisees of mine used to ask about how they could do "research."

I'm a bit skeptical, but with computers, things are more accessible.

loch

huh TIL

Eric Silva

isnt it mostly w combinatorial stuff

loch

i mean im aware of stuff like REU etc.

Ted Shifrin

REU's vary in their levels, but universities have been pushing undergraduate research hard the last decade.

When I was an undergrad and took 10 graduate courses, no one thought about it.

Eric Silva

i had a "research" assistantship w Neves, but that was essentially just a hard reading course i got paid for

loch

00:47

i see
this is not a thing in the UK - at least where i did my undergrad/masters

Daminark

What we do here in the REU is usually not research as far as I know, except some superstars + some folk who do stuff about finite spaces

Ted Shifrin

I can see virtues of it, but I can also see it as part of the dumbing down of our undergraduate curriculum.

geocalc33

I think i might buy a textbook, read it and try some of the exercises

Daminark

But I find that the majority of the projects are just, learn some math and write about it, usually stuff that's already known. In a way I feel like it's meant to be a replacement for places that have a senior thesis

Ted Shifrin

geocalc, when you get to differential geometry, my book is free. :)

geocalc33

00:48

okay,

Ted Shifrin

Demonark: I don't call that research. I call that a reading project. I've directed plenty of those.

Eric Silva

@Daminark tbh i wish he had theses tho :(

geocalc33

I think i actually have the prereqs and my uni to take diff geo

user441848

Hello. I have a question. Is it normal to not to remember almost anything from a mathematic course taken 2 and a half years ago?

loch

@geocalc33 there are a lot of free books/resources available on the internet - in case you don't want to spend money (textbooks can be expensive)

Ted Shifrin

00:49

it's a challenging course, geocalc, but the prereqs are multivariable calc and linear algebra.

Daminark

Theses are usually longer term than the REU, yeah?

geocalc33

yeah i took those

Ted Shifrin

@user441848: Yes, if you don't use the stuff.

Eric Silva

@Daminark ye bruv

geocalc33

use it or lose it

or would you prefer synaptic pruning of the dendritic spines

Daminark

00:51

Hmm, that could be interesting as well. But oh well :/

user441848

@TedShifrin what a relief, I was already worried. I took a discrete mathematic course 2 and a half years ago and at this moment I cannot remember not even 1 definition from the course.

Ted Shifrin

anyhow, @Eric, if I can help in any way, let me know ... you should come cook for a week sometime :P

Eric Silva

i havent cooked in so long it's sad

ive meant to prepare feijoada before i was struck ill

Daminark

Does Soug not even give time for that?

Ted Shifrin

In general, at my prior university, we tried to tell people that if they hadn't taken the prerequisite course within 2 semesters, they needed to retake it, @user441848.

Eric, we can't have that!

geocalc33

00:53

oh that applies to me

Eric Silva

@Daminark what

geocalc33

i have to retake all my classes

Daminark

Cooking

Ted Shifrin

LOL ... or do some very serious reviewing, geocalc.

Eric Silva

no i was sick

so i was struggling to get up to cook for myself

Daminark

00:54

@Ted huh, I've never heard of that kinda rule before, though I also don't know of too many scenarios where this situation played out

Ted Shifrin

Demonark, it's hard to enforce, but if you wait more than two semesters after Calc I to take Calc II, as some people do, you're gonna have issues.

2

user441848

@TedShifrin ok that's good to know

Ted Shifrin

OK, off to cook dinner. Good to see you, Eric. And get better. Hugs

Daminark

See you Ted!

Ted Shifrin

See ya, Demonark.

Eric Silva

00:56

fare thee well @Ted

user441848

bye Ted :-)

loch

see you!

geocalc33

bye

Ted Shifrin

bye, all.

Eric Silva

@Daminark what have u been doing for the reu

Daminark

00:58

Working toward a proof that if $F$ is an abelian extension of $\mathbb{Q}(i)$, then $F \subset K_n$ where $K_n$ is given by adjoining torsion points of $y^2 = x^3 - x$

Eric Silva

cool

Daminark

For now I'm mostly just picking up background in ANT. How's SPDE going?

Eric Silva

alright i guess

im reading some paper by watanabe on approximating SPDE by PDE

Daminark

I see

Tanner Swett

01:20

I've noticed that it seems like any convex quadrilateral can be transformed into any other convex quadrilateral in a way which preserves collinear points.

I've looked on Wikipedia and it looks like this is called a homography... or maybe a collineation... or maybe a perspectivity.

Whatever it's called, do such transformations preserve ellipses?

This question is motivated by a drawing exercise.

To do the exercise, start by drawing the vertices of a convex quadrilateral ABCD, then draw the edges of the quadrilateral.

Next, draw the diagonals of the quadrilateral, intersecting at a "center" point E.

Then draw a line segment which passes through E and is parallel or concurrent to edges AB and CD, terminating on edges BC and DA. Call the termination points F and G.

Do the same with the roles of the edges interchanged. Call these termination points H and J.

Finally, draw an "oval" passing through F, G, H and J, tangent to all four edges of the quadrilateral.

The question is: is the resulting "oval" always an ellipse?

I attempted the exercise with this quadrilateral, and the oval certainly doesn't look like an ellipse. But perhaps I just didn't draw it accurately.

geocalc33

What if the quadrilateral is a square?

Tanner Swett

Well, then you'll end up with a circle.

geocalc33

01:35

so are you ruling that out

Tanner Swett

I'm considering a circle to be an ellipse.

geocalc33

oh okay

didn't know that

Daminark

So I probably can't stay for long enough to really help out

But what does "concurrent to edges AB and CD" mean? I've never quite heard that term before

Oh I think I get it, so if AB and BC aren't parallel

Then you extend them to a line and then draw a line from that intersection point to E?

If so, I think the answer is that this won't give you an ellipse, try doing it on a trapezoid

Basically, the point of intersection of the diagonals should be a bit "high" (the point E) but centered horizontally. Now, when you draw your F and G, you'll see that FG is a straight line that's closer to AB than to DC, and that would play the role of one axis of the ellipse, and then HJ would play the role of the other axis. But E is closer to H than to J, while I think for an ellipse it should be equidistant

Anyway I gotta go do some work, and also you should ask people who know geometry better than I do, but this is why I think you don't get an ellipse in general. @TannerSwett

Tanner Swett

@Daminark That is what I mean by concurrent, yes.

@Daminark I'm trying this out in GeoGebra online, and I'm pretty much convinced that it will always give you an ellipse.

You said that FG "would play the role of one axis of the ellipse", but that doesn't seem to be the case.

Daminark

01:58

Oh I noticed this, and so the thing is, it's not clear formally what "the oval" means

Tanner Swett

Right.

It seems like there is, in fact, always exactly one ellipse which is tangent to the quadrilateral at the four given points.

Daminark

Oh you want it to be tangent. I'm much more willing to buy that now

No idea how a proof would look but now I'm a believer

Tanner Swett

Honestly, I still find it hard to believe that the intersection of a plane obliquely with a cone is an ellipse. :D

It seems to me like the end of the ellipse closer to the vertex of the cone would be "narrower", and the end more distant from the cone would be "broader".

Just like an egg has a narrow end and a broad end.

Daminark

Anyway I really should probably go but yeah this is interesting

Tanner Swett

Of course, the conic section is, in fact, an ellipse. Ellipses seem to be very resilient to various kinds of transformations, including whatever kind of transformation this is.

Tanner Swett

02:21

There's what my exercise above would have looked like if I had drawn it accurately.

Semiclassical

oh hey, geogebra

Rudi_Birnbaum

@TannerSwett Hi there, I once upon a time had a similar expectation. Maybe it helps you to consider that the end more distant from the vertex is at the same time "cut at a smaller angle" and thus one should expect it to get "sharper" at the same time. I alwasy was confused by the fact the the ellipse is also an "cylinder-intersetcion" with a plain.

Tanner Swett

@Rudi_Birnbaum Oh, that makes sense!

And it's not too surprising that the two effects cancel out.

Rudi_Birnbaum

yep

@TannerSwett Still, deforming the cylinder to the cone has some effect on the ellipse, not on the shape but on the map between the points on the ellipse. Maybe it could be interesting to explicate that function ...

rschwieb