Maths is Fun

aditya10r

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that's basic ... taught in 12th Bhai :p ...
.........................................................
In jee-15 i did not encounter a single inverse question and in 16 there was only one that too was a 2x2 matrix.

Never encountered a 4x4 one.
 

aditya10r

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:facepalm:Kitna chutiya hoon main?

Cos 2z is analytic.


Direct integration works. I was trying to substitute z=π*(e^iθ) with θ limits from -π/2 to π/2. From there it went way too complex (pun intended).

OTOH direct integration gave me answer = 4 Sin2πi

BTW, I was also seeing the wrong answer :doh:. The answer was not zero. I saw the answer of exercise 14.2 instead of 14.1
What book are you solving??

=========================================
 

Screambowl

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:facepalm:Kitna chutiya hoon main?

Cos 2z is analytic.


Direct integration works. I was trying to substitute z=π*(e^iθ) with θ limits from -π/2 to π/2. From there it went way too complex (pun intended).

OTOH direct integration gave me answer = 4 Sin2πi

BTW, I was also seeing the wrong answer :doh:. The answer was not zero. I saw the answer of exercise 14.2 instead of 14.1
or u substituted 2z = u ?


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

Adioz

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The Ultranationalist

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Nice thread. I am extremely weak in Maths. Someone help me solve this:-
View attachment 18524

Answer = 0
You haven't expanded it correctly .


Here for help.

COS^2x=(1+cos^2x)/2 and Sin^2x=(1-cos^2x)/2
:facepalm:Kitna chutiya hoon main?

Cos 2z is analytic.


Direct integration works. I was trying to substitute z=π*(e^iθ) with θ limits from -π/2 to π/2. From there it went way too complex (pun intended).

OTOH direct integration gave me answer = 4 Sin2πi

BTW, I was also seeing the wrong answer :doh:. The answer was not zero. I saw the answer of exercise 14.2 instead of 14.1

Give it a rest you geniuses, i thought it was going to be fun but now because of you i have strted to feel inferiority complex already:frusty:
 

Johny_Baba

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Feynman vs. The Abacus
This is an excerpt from the chapter "Lucky Numbers", in Surely, You're Joking, Mr. Feynman!, Edward Hutchings ed., W. W. Norton, ISBN: 0-393-31604-1.
The setting is Brazil; the narrator is Richard Feynman./
Link : http://www.ee.ryerson.ca/~elf/abacus/feynman.html


A Japanese man came into the restaurant. I had seen him before, wandering around; he was trying to sell abacuses. He started to talk to the waiters, and challenged them: He said he could add numbers faster than any of them could do.

The waiters didn't want to lose face, so they said, "Yeah, yeah. Why don't you go over and challenge the customer over there?"

The man came over. I protested, "But I don't speak Portuguese well!"

The waiters laughed. "The numbers are easy," they said.

They brought me a paper and pencil.

The man asked a waiter to call out some numbers to add. He beat me hollow, because while I was writing the numbers down, he was already adding them as he went along.

I suggested that the waiter write down two identical lists of numbers and hand them to us at the same time. It didn't make much difference. He still beat me by quite a bit.

However, the man got a little bit excited: he wanted to prove himself some more. "Multiplicação!" he said.

Somebody wrote down a problem. He beat me again, but not by much, because I'm pretty good at products.

The man then made a mistake: he proposed we go on to division. What he didn't realize was, the harder the problem, the better chance I had.

We both did a long division problem. It was a tie.

The bothered the hell out of the Japanese man, because he was apparently well trained on the abacus, and here he was almost beaten by this customer in a restaurant.

"Raios cubicos!" he says with a vengeance. Cube roots! He wants to do cube roots by arithmetic. It's hard to find a more difficult fundamental problem in arithmetic. It must have been his topnotch exercise in abacus-land.

He writes down a number on some paper— any old number— and I still remember it: 1729.03. He starts working on it, mumbling and grumbling: "Mmmmmmagmmmmbrrr"— he's working like a demon! He's poring away, doing this cube root.

Meanwhile I'm just sitting there.

One of the waiters says, "What are you doing?".

I point to my head. "Thinking!" I say. I write down 12 on the paper. After a little while I've got 12.002.

The man with the abacus wipes the sweat off his forehead: "Twelve!" he says.

"Oh, no!" I say. "More digits! More digits!" I know that in taking a cube root by arithmetic, each new digit is even more work that the one before. It's a hard job.

He buries himself again, grunting "Rrrrgrrrrmmmmmm ...," while I add on two more digits. He finally lifts his head to say, "12.01!"

The waiter are all excited and happy. They tell the man, "Look! He does it only by thinking, and you need an abacus! He's got more digits!"

He was completely washed out, and left, humiliated. The waiters congratulated each other.

How did the customer beat the abacus?

The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03 is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root's excess is one-third of the number's excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). So I was able to pull out a whole lot of digits that way.

A few weeks later, the man came into the cocktail lounge of the hotel I was staying at. He recognized me and came over. "Tell me," he said, "how were you able to do that cube-root problem so fast?"

I started to explain that it was an approximate method, and had to do with the percentage of error. "Suppose you had given me 28. Now the cube root of 27 is 3 ..."

He picks up his abacus: zzzzzzzzzzzzzzz— "Oh yes," he says.

I realized something: he doesn't know numbers. With the abacus, you don't have to memorize a lot of arithmetic combinations; all you have to do is to learn to push the little beads up and down. You don't have to memorize 9+7=16; you just know that when you add 9, you push a ten's bead up and pull a one's bead down. So we're slower at basic arithmetic, but we know numbers.

Furthermore, the whole idea of an approximate method was beyond him, even though a cubic root often cannot be computed exactly by any method. So I never could teach him how I did cube roots or explain how lucky I was that he happened to choose 1729.03.

-----------------------------------------------------------------------------------------------------------------------------------------------------

Now,a little life story of mine

When i was in 9th class i found out bout something called Abacus.I was so excited by reading bout it that i went to market and literally visited all the stationary shops and novelty stores to find one,but i couldn't find one at anywhere.In fact,almost all of them asked me,"Abacus ? What is it?".

A friend of mine happened to have an abacus that he received from his tuition tutor.I found his tutor who's running some math academy and asked me to sell one as i was also interested in it,but he demanded Rs.1200 for it.

I was like, :awman: Sir,me poor,me din't have that much moni,sir i don't think it is worth that much moni,sir pliz sir.

He: Ok,you may go.

:okay:
 
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Screambowl

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Summation notation
In this section we need to do a brief review of summation notation or sigma notation. We’ll start out with two integers, n and m, with
and
and a list of numbers denoted as follows,



We want to add them up, in other words we want,



For large lists this can be a fairly cumbersome notation so we introduce summation notation to denote these kinds of sums. The case above is denoted as follows.

 

Peter

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Erwin Kreyszig 10th edition.

Yeah 2z= u, then direct integration.
What is the answer???

You have written it as 4sin2(pi)i or is it just sin2(pi)i.
 

Krusty

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Ok this isn't a problem as such, but I have always been profoundly amazed and baffled at the same time by infinity. Anyone who likes Maths will surely appreciate this. I will upload some other nice documentaries later. I can't believe Ramanujan hasn't come up in any of the posts yet

A simple but a mind boggling concept...

 

Ancient Indian

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I have small question.
Did you guys solve any problem using computer?
I mean solving problem with computer. Like writing program and getting final answer.
 

Peter

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Which board did you do your 10/12th in? I was from a CBSE school and I was taught it. :shock:
In CICSE(ISC) we did not study Gauss Jordan elimination method. In JU BCSE they have that in first year.

P.S. We had actually being taught another method to solve equations by use of determinants.
 

aditya10r

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P.S. We had actually being taught another method to solve equations by use of determinants.
The one method in which you take some constant or variable common from any of the rows/columns.

===============================================================
 

Adioz

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What is the answer???

You have written it as 4sin2(pi)i or is it just sin2(pi)i.
:p
My bad, its Sin2πi

Which board did you do your 10/12th in? I was from a CBSE school and I was taught it. :shock:
I did it in a CBSE school and was introduced to matrices in 12th class. But they taught system of equations, multiplication, inverse (by co-factor method), etc. Gauss-Jordan was not taught :confused1:

I have small question.
Did you guys solve any problem using computer?
I mean solving problem with computer. Like writing program and getting final answer.
Wrote one (was forced to write) in MATLAB:-
disp('Program to find perimeter of circle and error in it');
disp('All units are in mm');
q=input('Number of parts to divide circle: ');
r=input('Enter the value of radius: ');
S=2*r*sin(pi/q);
P=S*q;
fprintf('Perimeter of circle is: %f\n', P);
p2=2*pi*r;
e=p2-P;
if (e == 0)
fprintf('No. error in calculation of Perimeter');
else
fprintf('Error in Perimeter of circle is %f\n', e);
end

:troll:
 

Screambowl

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@Adioz
@Peter

My apologies. You are right. I learnt Gauss-Jordan method during my prep for IIT-JEE. Not under CBSE

hain?
you don't have it any more in 12th cbse??
we had one whole chapter of matrix n determinants.. row column interchange for solving linear eqtns..
 

Krusty

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hain?
you don't have it any more in 12th cbse??
we had one whole chapter of matrix n determinants.. row column interchange for solving linear eqtns..
Not 'Not anymore'. 12th was a Long time ago for me. Maybe they do now, I am not sure. And tbh, I never concentrated on my school studies. JEE prep took almost every minute back then. Still I failed to tame that beast :laugh:
 

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