@Obliv yes. Lagrange multipliers are just a way to solve for places where the gradient is zero when constrained to a curve. Whether you're at a max or min is unknown.

@rob @heather you both owe a dollar to there pun jar.

@DanielSank, $\sum$ people like math puns, $\sum$ people don't.

@heather ::cringe::

=)

@rob I gave an incorrect definition of a tangent plane (not surprisingly since this material is still new to me). It should be $\nabla f(u) \cdot (x-u) = 0$ for some point $u$ and both $g,f$ are normal to $\nabla f$ and $\nabla g$ for this to occur

For all who love math puns: chat.stackexchange.com/rooms/71/conversation/…

@Obliv aha, I was just talking to rebecca about this

I sort of understand my confusion now. Sort of. I really need to look into this more.. @0celo7 who is that, your mom?

gf

I don't refer to my mother by her first name...well I do, but it's not rebecca

Good friend?

@Obliv yeah she's a good friend

Why do you refer to your parents by their first name?

Because we're all adults?

That's really sane and cool @0celo7 too bad my family doesn't operate that way. mom,dad are titles we refer to them by for 'respect'

Oh they get mad at me when I do it :P

But doesn't stop me

Well I think that's the right way to go eventually (maybe mid-late 20's)

@Obliv It's a normal thing to call them "mom" and "dad"

My parents call my grandparents that

It's just respect

@0celo7 so is rebecca better at math than me? :(

then again who isn't.

besides @sirC

rekt

dog

flagged.

^ that

oh

lol @SirCumference hehe

@Obliv She's done less math so I don't know

@sirC lmao.. I'm kidding btw but if you see 0celo7 say that I'd edit just in case. :P

@Obliv I know :P

yeah you've experienced his wrath first hand.

Not taking that seriously, but yeah you're definitely right

I've got catching up to do before I'm up to you guys

I'm on my way though. Those notes are pretty helpful.

@heather so do you know what a manifold is now?

You know, back in middle school I was learning how to differentiate between facts and opinions

Not differentiate functions

@sirC I was playing videogames and b.s.ing my pre-algebra homework

@0celo7, erm, not really. I was working on algebra II/pre-calc

@0celo7 Dude, you and your manifolds.

She's in middle school, for heaven's sake.

@Obliv You didn't take algebra in middle school?

literally seconds before class I'd scribble random things onto the paper and when he'd come around to check the hw he'd just nod and move on. Sometimes he'd notice and then give me a nice stern look ;P

@DanielSank She wanted to know what a manifold is!!!!!!!!

@Obliv Haha, neat

And I didn't even use a technical definition

I did take algebra 1 in 8th grade I think. yeah I did @sirC

There's a nontechnical definition?

@DanielSank, yeah but manifolds sound cool. And yeah I asked about the manifolds.

@0celo7, there's a nontechnical definition?

@heather They are cool. A manifold is anything where if you look at a small enough piece, appears like an n-dimensional space.

Gluing together $\Bbb R^n$s is nontechnical.

@0celo7, I'm still not quite clear what it means to "glue together" those.

Math glue. It's part of glue theory.

For example, a string is a 1D manifold: every piece, if small enough, looks like a plain ol' 1D space.

@SirCumference, I'm going to assume that's a joke?

@heather Well...the technical definition of glue is a quotient space, but that's not what's actually going on :P

@heather Yeah, it is

The surface of a balloon is a 2D manifold: if you look at any small area, it looks like a normal 2D space.

A doughnut is also a 2D manifold: any small patch looks just like a 2D space.

@DanielSank, oh, okay. So a 3D manifold would look like normal 3D space on the small scale? So maybe...oh, would a hypercube be a 3D manifold?

@0celo7, quotient space...?

A manifold is just anything where each little piece can be modeled as an n-dimensional space of real numbers. In other words, it's anything where each little piece can be given a coordinate system involving n coordinates.

@heather That's technical.

@heather "Hypercube" usually means a 4D cube...

No, a cube is not a manifold.

@0celo7 Don't start with me, bro.

@DanielSank, yeah, and each "side" is a 3D cube, right? So it would look like 3D space...?

@DanielSank ?

@heather There are issues at the edges and corners.

It's not a manifold. A manifold must be "round"

@heather Oh uh... yeah that might be right.

@DanielSank No!

@0celo7 Woah...

Ok it's wrong.

The idea is right though

@0celo7, oh, that makes sense. Which is why a balloon works, but a hypercube doesn't. Okay.

@heather here is a 1D manifold: \

Here's another one: u

Here's another one: o

Each of those shapes is a 1D curve at each point.

Are you trying to give me an aneurism

But the v isn't curved, right?

Here's something that's not a 1D manifold: X

So it would be more like a u?

And x isn't because it crosses?