TT's Maths Thread

[TrueTears]

where is a spherical wedge given by

Now I understand what that means, however if we extend this to a more general spherical region such as:



What the hell are and ?

If and are a function of spherical coordinates, then where is the ?

[/0]

Hmm it should be right?

[TrueTears]

Hmm it should be right?

nope just and

page 1008 if u wanna double check

[/0]

But if you integrate there will be a leftover after integration

[TrueTears]

hmmmmm weird...

[Cthulhu]

I was reading through this earlier and I couldn't figure it out. The only thing that I could think of was some sort of limit that is beyond my late night math thinkedness.

[Mao]

So what is the geometric interpretation of a triple integral. Say:

Check out Stoke's theorem. It can give a surface area.

[TrueTears]

So what is the geometric interpretation of a triple integral. Say:

Check out Stoke's theorem. It can give a surface area.

Thanks! I'll check it out.

I was reading through this earlier and I couldn't figure it out. The only thing that I could think of was some sort of limit that is beyond my late night math thinkedness.

haha, yeah I think I got it now, p isn't mentioned because it is already restricted.

[TrueTears]

Ahhh I've decided to visit my good ol maths after a few month hiatus...

Anyways was playing around while I was bored of commerce study tonight and I seem to have forgotten how to prove the triple integral formula...



where is the Jacobian of a transformation T

Any enlightenment would be good xD

[TrueTears]

Ahh enough economics reading, time for some late night maths, very nostalgic haha, was flipping through AnC and came across this pretty one, I've started by applying AM-GM, but some more ideas would be wonderful xD

Let , find the least constant C such that for all , .

[TrueTears]

brainless stream of consciousness... after a long period of accounting reading xD

Suppose that at most two of the , say and , are nonzero. Then the left-hand side of the inequality becomes and the right-hand side becomes .

By AM-GM,



Suppose that our statement holds when at most k of the are equal to zero. Suppose now that k+1 of the are equal to zero, for . WLOG, let these be .



We wish to show that by replacing the with the , we increase the left-hand side of the desired inequality without changing the right-hand side, then we can use the inductive hypothesis...

soo ehh, how to complete the induction, i feel like im missing something...


kamil, /0 any ideas?

[TrueTears]

Probability paradox

You are participating in a game show where you are given the choice of three doors: Behind one of the doors is a Mazerati, behind the other two doors are goats. You pick a door and the game host, who knows what is behind the doors, opens another door which has a goat. He then says to you, "Do you want to switch to the other?" Is it better to switch at this point or to stick with your original choice or maybe it does not matter?

Eh shouldn't it not matter what door you pick?

But that's not the right answer... how do you do this question?

[brightsky]

Yeah it's always better to change. For simplicity's sake, let's call the doors with goats inside them Door A and B, and the one with the Mazerati in it, door C.

Case 1: You choose Door C.

Then you would be shown either Door A or Door B which has a goat inside it. Obviously, if you switch, you do not get the Mazerati, and if you stick with your original choice, then you do get it.

Case 2: You choose Door B.

Then you are shown either Door C or Door A, Door C which has the Mazerati in it. In this case, if you stick with your original choice, you don't get the Mazerati, and if you switch, you do.

Case 3: You choose Door A.

Then you are shown either Door C or Door B, Door C which has the Mazerati in it. In this case, again, if you stick with your original choice, you don't get the Mazerati, and if you switch, you do.

These are the ONLY 3 possibilities that can happen. As you can see, there is a 2 out of 3 chance you will pick Door B or Door C, and hence will need to switch to get the Mazerati, and only 1 out of 3 chance you will pick the right door.

Hence why there is a bigger possibility for you to get the Mazerati if you switch.

[TrueTears]

i still dont get it =S

if u picked door C then if you switch u have a 2/3 of getting a goat, isn't that worse off? u have a higher percentage of losing.

if u picked door B then u have a 1/3 chance of getting the car or 1/3 chance of picking door A to get the goat, so isn't it equal chance?

[brightsky]

i still dont get it =S

if u picked door C then if you switch u have a 2/3 of getting a goat, isn't that worse off? u have a higher percentage of losing.

if u picked door B then u have a 1/3 chance of getting the car or 1/3 chance of picking door A to get the goat, so isn't it equal chance?

Look at it from a broader spectrum. Start from step 1. You choose a door. Now there is a higher possibility that you will choose the door that doesn't contain the Mazerati. Because there is a higher possibility of this happen, this in turn means that there is a higher possibility that if you switch, you will get the car.

if u picked door C then if you switch u have a 2/3 of getting a goat, isn't that worse off? u have a higher percentage of losing.

But you need to compare the chances with Door A and B as well. It is MORE of a chance that you will not pick door C. Hence switching would mean that you are more likely to switch to the door that has the car. Yes, if you pick door C and switch, you will lose, but that is only 1/3 of the chances.

if u picked door B then u have a 1/3 chance of getting the car or 1/3 chance of picking door A to get the goat, so isn't it equal chance?

If you pick door B and you switch, you'll get the car. If you pick door A and switch, you'll get the car. If you pick Door C and switch, you don't.

If you pick door B and don't switch, you lose. Same deal for A. If you pick Door C and don't switch, you win.

Calculate the chances from here.