Room for Inceptio and Isomorphism

Inceptio

04:29

Hello. Good morning. Are you on this question?

Isomorphism

yep

got it.. but was too late :(

Inceptio

People(Potato) is too fast, indeed! :P

Isomorphism

he he

Now I am on math.stackexchange.com/questions/396935/…

Inceptio

I'm on that, too. Seems like a 'irrational' day!

*an! (Grammar).:P

Isomorphism

lol

Will serve as good Olympiad questions :P

Inceptio

04:43

Yeah. RMO level, maybe. INMO guys will crack it in 10 min. ;)

Isomorphism

true true..

Inceptio

Are you trying to get a solution or proving them irrational?

Isomorphism

Well, I converted it into a diophantine. I am trying to find a solution...

Inceptio

This is interesting.

$x^4+y^2=z^2$ hasn't got any solutions in integers. How about rational solutions?

Isomorphism

05:21

i was trying rational only

But...

:(

I wish I had matlab...

Ah... there is another interesting question: Do you know a circle in the co-ordinate plane that misses all the rational points?

Inceptio

The same question put in another way, isn't it?

Isomorphism

hmm.. is it?

i dont think so

this question is stronger

What I am asking is simpler...

Inceptio

Look at my answer. I'm not quite sure. That's not very rigorous.

Graph of x^4+y^2=1 gives a weird looking graph.

Is it enough? Or do I need a more stronger statement?

And I don't think there is such circle.

Isomorphism

05:43

wait

I was answering something else

Inceptio

Cheating, man! :P

Isomorphism

:)

considering your last step... Did you have a simpler explanation than math.stackexchange.com/questions/153546/solving-x4-y4-z2

Inceptio

.. Those are trivial I believe. Using the fact : 'No right triangle with integral sides has area that is an integral square.'

Isomorphism

05:58

Try math.stackexchange.com/questions/396950/…

Anyway, I have not heard of the right angled triangle area thingy before..

Inceptio

That's Fermat's corollary ..

Woah. This has got such a nice closed form solution. :O

Isomorphism

I am surprised it is even true.. Let me try some numbers!

Inceptio

06:18

Are you trying that?

Isomorphism

well.. I am thinking about it... (and doing some extra work).

Did you find an interesting problem?

Inceptio

Integral, one?

6

Q: How can I calculate $\displaystyle \int \frac{\sec x\tan x}{3x+5}\,\mathrm dx$

How can I calculate $\displaystyle \int \frac{\sec x\tan x}{3x+5}\,\mathrm dx$ My Try:: $\displaystyle \int \frac{1}{3x+5}\left(\sec x\tan x \right)\,\mathrm dx$ Now Using Integration by Parts:: We Get $\displaystyle = \frac{1}{3x+5}\sec x +\int \frac{1}{(3x+5)^2}\sec x\,\mathrm dx$ Now My...

Isomorphism

that does not have an elementary function answer!

Inceptio

Or this one. It will be so difficult to discuss the solution in the class.

Isomorphism

we cant discuss this in class because most 12th std people do not know contour integration.

Thats the most powerful integrating tool

Inceptio

06:27

This is fun.

Isomorphism

we did that in class :)

If you want fun integrals (and almost inexhaustible collection at that!), check out Kunny in mathlinks site

See artofproblemsolving.com/Forum/resources.php?c=87&cid=184

Join that site... It has awesome IMO questions too

Inceptio

The question we discussed was so ready-made . :P None would think of substituting x=tan y, unless it is Chris's Wise sister(The question was asked by him/her, ironic).:P

I know, I have been there. Didn't sign up. Looked pretty boring.:P

Isomorphism

the forum is boring... but Kunny's integral collection is the best there

By the way, whenever you see $1+x^2$, there is a pretty natural itch to substitute $x = tan \theta$, so I would say that the substitution was ready made as well :P

Inceptio

Check his answers. He is too good at integrals.

Isomorphism

Ah! Yes I know

Inceptio

06:38

Okay. . Give the same question in the class today. Lets see how many come up with complete solution. (I won't answer.:P)

Isomorphism

Please... your class...(Sigh) only two or three people are awake... I will try it with the other class as well!

Inceptio

Are you up-voting my previous answers? :P

Isomorphism

I was

Not today though

Inceptio

Well, yes. Our class' has got Chemistry as their favorite subject.;)

Isomorphism

:( :(

Inceptio

06:41

Someone else' is digging my profile. :P

Isomorphism

Kewl

Inceptio

Tell me ONE good thing about chemistry?(Other winning noble prize in that :P )

Isomorphism

Dude, I am not the best person to ask

I was trying to figure that out too.

Inceptio

What are you doing right now? Post graduate in ...?

Isomorphism

Now I just dont bother :P

Ph.D in Electrical Communication

Inceptio

06:43

Is that fun?

Maybe you should more details in your profile. (You will get a Autobiographer badge :P)

*an.:(

*add . ah!

Isomorphism

I want to be a math Ninja

Inceptio

Sounds great. . You should start proving Riemann. :P

Which question are you on now?

Isomorphism

none

I am setting que. papers for you people

Inceptio

Question papers? For discussing?

Isomorphism

07:01

nope

practice tests

Wait!

Riemann??

A math Ninja is someone who secretly 'math's. His identity is not supposed to be known...

Inceptio

07:20

Yeah . I know. User17762 is math ninja for instance. :P

Practice tests? We will be having integrals' test? At last, had three chem tests in a row.

How do you integrate this?

Isomorphism

i cant read that

Inceptio

latex.codecogs.com/gif.latex?$\int_{-\pi}^{\pi}\dfrac{\cos^2&space;x}{1+a^x}dx

That isn't appearing properly. How do you use latex in this room?

Integrating (cos^2 x)/(1+a^x) from -pi to pi.

Any hints?

Inceptio

07:57

Are you still there?

Isomorphism

09:16

Ya...

Inceptio

I'm struggling with that integral.

And yeah, a question in your complex numbers DPP. I still don't get it how.

Proving that average of k sin k(k=2,4,6 ..180) is cot 1. How's it solved?

Isomorphism

09:49

dude for that integral, just use the f(a+b-x) trick and add the integral to itself and write it in two different ways,

Inceptio

The limits are -pi to pi, you get 0 when you add it. How you go about now?

Isomorphism

so replace x by -x

Now a^{-x}

Inceptio

Oh. Okay how about the complex number quest? Any hints?

Inceptio

14:48

Look at the second solution. I was about to hint you about expanding sin(101x). My bad! :P

Transcript for

$Mathematics$ Room for Inceptio and Isomorphism