Strange wall-ball problem

Okay I get it - the title is not that imaginitive.
Hi there! The organic post that was to be never came up because I left my copy back in school but its some pretty interesting isomerism nuts that I was shown by my teacher. For now its some physics- collision style!
In fiitjee and other study mats there is always this obscure thing that concerns a ball with a wall. (Wall=infinite mass, ball=m)When the ball collides with the wall having an initial velocity u it returns back with the same velocity provided that the collision is elastic. Now fix the ball, let the wall strike the ball with a velocity u.Whatt happens now?

Contrary to all common sense the ball lurches forward with a velocity 2u.why??
A friend of mine kaustav sengupta (never mind the too erudite tone of the sentence) made sense when he said that consider the first case as in figure1, the frame instead of being stationary with respect to the ground is having a velocity u to its right. then?/Â…..we get the second case, fig2, minus the comment about not making sense.
Comment if u knew it
Comment if u did not
Comment if u think itÂ’s wrong
Comment anyway!

the return of sith :-)

hi there! i came back from skool yesterday and went through the whole blog. the idea was great i think.to start a blog that lays importance to the subtle nuances of physics and maths(not much of a chemistry there).and i m rlly happy that the posts have not dried up.as per catching up - it was good to hear that ftse was actually a mess. u know wat? a friend of a friend of mine,mutual friend that is, reads in fiitjee delhi classroom courses and he told us that they were taught in advance in the discussion classes abt 80% of the sums - a leak if there ever was one.assuming of course that he wasnt, u know, throwing off.anyway i was down in confidence for weeks.sort of brings things into perspective, doesnt it?
anyway i will be posting one on organic pretty soon - its been neglected for long.
pss:i will be staying here till 27th.then i wont come back to home till march.

Whatz prooved & Whats not :: A DEAD END SUPPLIMENT !

Hey all !

Hmm ...
Another Dead End ? Nope I'm saturated of those now. But this one's interesting enough to be brought to notice of the blog.

A seemingly remarkable proof indeed for prooving that all numbers are interesting !
But Can a subjectivity of the problem be discussed mathematically ? The answer seems to be yes !?!

Now lemme introduce you 2 a couple of DEAD ENDS :

(1)

To Proove : Every natural number N can be described within 15 words.
Assumption : Let there be a set S of number which cannot be expressed within 15 words.
Ordering the set S & pickig out the first element, say P we get P as :
P is the "the smallest natural number that cannot be unambiguously described in fifteen words or less".

:. P can be described within 15 words.
By Reductio Ad Absurdum ;
We herey proove the Statement that :
EVERY NUMBER CAN BE REPRESENTED WITHIN 15 WORDS.

(2)

I begin this one, relating to the THEOREM OF MATHEMATICAL INDUCTION as quoted by Arun in a comment to the previous post.

"

The principle of mathematical induction basically is a logical proof of extention. If you can show that:
1) The statement is true for the base case, i.e. 0 generally,
2) That if it is true for n, n-1, n-2, it IMPLIES truth for n+1.

"


Okay. Let there be a statement S(n) depending on n which can be either TRUE or FALSE.

I DEFINE S(n) as :
S(n): "In ANY group of 'n' blog-members, all have equal ages."
OR
"In a set of blog-members-ages from ANY particular blog, all values are equal."

Now proceeding on the lines of the above discussed theorem, lets discuss S(1).
: " In ANY group with 1 blog-member, All blog-members have equal ages ( Takin one member at a time since n = 1 )."
Clearly S(1) is TRUE.

Assume that S(k) is TRUE which implies that :
: " In ANY group of 'k' blog-members, all have equal ages."

Now to proove S(n) for all N belongs to (1,infinity), We must proove S(k+1).

So now we have a set of (k+1) blog-members. Of those, we can choose different combinations of 'k' blog members. In each of these combinations, all blog-members would have equal ages. Therefore, All blog-members in the (k+1) blog-member set are equal in age.
:. S(k+1) is TRUE if S(k) is TRUE.


S(1) is true. S(k+1) is TRUE When S(k) is TRUE.

:. by the THEOREM OF MATHEMATICAL INDUCTION ...

S(n) is TRUE.

Implying this for the blog KVPY2005 : Fused Bulbs... I hereby proove that all memebers in this blog are equal in age, which is conincidentally true within the limits of error. lol.



Ill leave the implications to be discussed by the blog members.

WAITING FOR COMMENTS

(desperately hehehe)

Twish

Boring Numbers?

Hey. It's been a long time since I've posted anything, so I'll make a candid proof I saw on the net somewhere.

This deals with a really fundamental theory:

There is no such thing as a uninteresting number.

As we deal with the earth-shaking proposition, one must have a deep fundamental knowledge of sets. Let us limit our theory to the infinite set of natural numbers.

On with the proof:
Let N be the set of all natural numbers, of which X represents the set of uninteresting number. First let us order this set X in numerical order. Let us now analyse the first number of this set. Our understanding of what makes a number interesting is so fragile that to produce such an example is a great step forward. Thus this number being the FIRST uninteresting number is of vital importance, bringing our interest to it. Thus it can not belong to the set, and isn't the first element. Let X' be the revised set omitting this fraud. Thus the second term of set X is the first of set X'. We can apply the same reasoning here, and easily omit this element, and continue to do so for all other numbers of the set, making it a null set. Thus it is easily proved that there is no uninteresting number.

Lovely proof isn't it? But there does exist a very important logical consideration. If one considers ONLY the negative numbers, our present ordering is befuddled, but do not panic. Suppose we order them in REVERSE order, letting greatest come first. Thus we can proceed by the same steps as above.

Now, we come to a very important juncture. If we combine these two sets, and look at ALL integers, we're stuck. For sure the negativity is an important difference between '+' and '-' numbers, and we can't ignore it. A set of Z has no beginning or end, so we CAN'T order it, and use this lovely proof for it. So it seems that the interesting-ness of certain '+' or '-' numbers makes other numbers loose there interesting-ness. But I thought interesting-ness was an intrisic property of a number. I.E. that a number can be called interesting because of a property that it exhibits, i.e. primality (it being prime) or it's square-ness/cube-ness/n-power-ness, or a pattern exhibited by its digits (like 12321).
Appealing to this logic, we could either conclude two things: That there exist no uninteresting numbers, or that the interesting-ness of a number does infact depend extrisicly as well as intrisicaly, and that it depends on a negative counterpart (whether that is the negative of the same number or not can not be concluded though).
As much as I'd like to take the latter, for it's more complicated, and that it IS earth-shaking in its statement, I'll abuse Occam's Razor and say that the former is obviously true.
Occam's Razor is: All explanations are simple, and the more complex one is more probably wrong. Note the keyword: Probably. It's generally quoted with overexagerrations like:
When you see a reflection:
1) Light is getting reflected
2) There is an alternate reality, which can be entered through the window, and which is inhabited by people who look EXACTLY like you, and happen to do EXACTLY what you are in front of the mirror.
Sometimes I think that life would be a lot more fun if it weren't so obviously 1.
That's all for now. I hope to be back this weekend with a post on the brain.
Signing off and Id Mubarak,
Arun

BEFORE THE BEGINNING AND BEYOND THE END (PART 2)

Hello again all of you. I am back, with a spicy second part of my article. The contents of this article as well as the one it follows is a collection of well laid facts cemented with the author's own ideas. Thanx 4 reading guys, enjoy. Please refer to the previous section wjenever in doubt.


Let us now extend our view of the symmetry about the big bang, we can go forth to say that the previous universe too must have originated from another big bang. Therefore, this brings us back to the concept of oscillating universe theory. However, the problem with oscillating universe is Entropic considerations. The problem is the following:

The oscillating universe theory says the entropy of all the singularity states of the universe have same entropy. Now let us assume the whole of the universe as one system. Suppose right here right now, I drop an egg and break it. I have thus increased the entropy of the universe. However, when our universe reaches its next big crunch, the entropy has to be same as that of the last singularity. There is the problem, entropy remaining constant although the system is experiencing an irreversible process. I will try to provide an explanation for it.

All of us know about supernovae explosions. Some parts of a dying star blows off as a huge explosion into the realms of the vast universe, and the remaining collapse into a tiny dwarf star. Let’s apply this logic to the entire universe.

Let S1 and S2 be two singularity states. A big bang at S1, expansion, and then contraction and finally a big crunch at S2 are the sequence of events. The change in Entropy is ΔE. According to Boltzmann postulate or the definition of Entropy,
ΔE = kb (ln Ω1 - ln Ω2) where, the sigma are the no of ways in which the same microscopic arrangements can be restored from a starting state.
So what we do now is very simple. We ‘transfer’ all the disorder in the whole of the universe to say a few moles of gas molecules. We outcast there molecules and allow the rest of the universe to move into singularity 2.

Let me make this more lucid. While playing billiards (or pool or snookers ... whatever), on a perfectly friction less table, we first break the triangular arrangement in the middle by a slow strike, the balls go a little haywire and keep moving and colliding with each other. As these collusions continue, the entropy is constantly increasing with time. But there is a remote possibility that say seven of these balls will again come back and form a tight arrangement. The remaining two will remain in a state of even increased randomness. Thus we can say that the entropy got localized to the two balls or got transferred from the other seven balls to the two.

This is one way in which we can satisfy both the oscillating universe theory and the second law of thermodynamics. But this too has a lot of problems of its own. First and the most important is that it is unable to explain the birth of the universe (I am talking about the real birth – the first big bang) and it too says that there has to be some thing beyond our universe.

It says our universe is constantly losing its mass into darkness (dark energy?). It predicts a very gruesome death to our lovely universe. A heat death scenario – a situation when there will be no energy gradients and hence there will be no process. (All processes require flow of energy.) But certainly it has done one good thing for sure, it has increased the life span of our universe to much beyond of what Big bang theory had proposed. It never says that the Big bang theory is wrong but it says that the big bang was not the beginning but only a phase change in the history of our universe.

I will not end this article with a conclusion as conclusions are for the readers to devise. It is a philosophical question and until we find a proof we can only speculate. We are like a child who presses its nose on a mirror, accepting it to be window. He knows it is not the reality. It is only the preconception in his mind. Reality lies beyond the glass- break it open. But he is afraid that in the process of breaking open the mirror and discovering the reality, he will destroy his well constructed sand castle.

Saurya Time Mishra

PS: Sorry if u couldn't c the comments before. Dunno y, but still, u can add them now!

~Gr81~

Diwali

Hello Everybody!!

Well, my Exams are over and I'm enjoying this festive season. Hopefully u ppl are enjoying too!

So ppl:

दीपावली की ढेर सारी शुभकामनाएँ!!

____________0____00___0____________
____________00_______0000__________
_____________000000000000__________
________0______000000000___________
____000000000_____00!______________
_____000000000___________000000____
_____00______00_________000000000__
______________00_______0000__00000_
______________00_______0!______000_
_____________000___00000________00_
____________000__00000000________0_
0________0000000000000000________0_
0________00000_0000____00________0_
00________00____00_____00________0_
00_______________00____00_______00_
_00______________000___00_______00_
_00_______________00___00______000_
__00______________000__0000000000__
___00____________0000___00000000___
____000__________0000____00000_____
_____0000______00000_______________
______00000000000000_______________
________0000000000_________________

We all know that busrting crackers pollutes our environment. But who cares about the "E"-nvironment?

So blast as many "E"-crackers as you want, and "E"njoy this "E"-Diwali!!

E-Diwali!


And yeah, more important stuff HERE:

Now I have a few days time, so tell me what all do you want to change in the blog....
Like:
- Add Intro
- Decrease no. of Posts visible
- Change theme (to what?? plz suggest...)

Write any kind of suggestion (ANYTHING... even something like flashy links...)

So waiting for ur suggestions!

PS:
Are u busy? If not, mayb u should see this:

• LOGAN's Mystery Of Time And Space Adventure [Mystery Game]
• Pencilmation [Cool Stick Figure Animation :D]

--

रसज्ञ शर्मा
* Rash thegr81!! *

Modern physics and Vedanta.

Ok, I agree the topic seems to be a turn-off but the ensuing article might just not be one. Actually I read a book of the same name by swami jitatmananda (a gem by all accounts –google him if u like). That along with a few observations of mine constitutes this post. So, back to the topic .Vedanta defines maya as sthana-kala-nimitta (ie space time causation). Without either one of these the other one has no meaning – nor does maya. Rings a bell –einstein’s space time continuum et all?-it should.
There is also the question of consciousness. It has already been mentioned in the Upanishads (or vedantas for that matter they are the same), that consciousness/awareness/opinion, whatever one may call it, affects the surroundings. And it has only recently been proved that the outcome of an elementary experiment (which can have only 2 outcomes) can be affected if the scientist conducting it has a biased opinion –all this is actually much more complicated than it sounds- but that’s that. There are similar mergers in oriental philosophy and occidental science that are increasingly evident even as we speak. Scientists like john a. wheeler have coined mouthful names for the phenomenon but I left the book at my hostel so I cannot quote. But this still might open avenues of thought open to many of u. and if u ask me, gita seems lifeless to me- Vedanta packs in much more excitement & cloudy aura. Issue a translation from ur library and go through it. Gita, on the hand was a part of Mahabharata which was purely a literary creation. Gita, once translated seems bland but yeah it uses devices and metaphors well. I don’t know that much Sanskrit but ppl seem to go gaga over gita – its just common sense! Or thus I think,well then each to his own.
How do u ppl like resonance though? For me some articles drive well, while most yield a tangent (vidyapith colliloquy for did-not-quite-get-that).
Now look here I am absolutely greedy on feedback so do comment.

latest intro

My pic!

The first hi-mates. I know I am the last un, but cant help with being in skool can I?So here is my intro.
Name: debanjan basu
Nick: my classmates call me basu (with that inimitable undertone of contempt-u know the sort)- n I am fine with that.
Identification: Kept me thinking actually coz I did not do anything special(read stupid) over there but the pic may help. Oh yes......I am from Ramakrishna mission vidyapith, deoghar .that'll do, wont it?
So that's all , as twish correctly pointed out, we shall all get together nxt summer.

BEFORE THE BEGINNING AND BEYOND THE END

Part 1

There was nothing at all, no space no time (not even me), then all of a sudden it all happened - The Big Bang. A theory we all have believed so blindfolded. A Theory that created a bigger bang in the world of science than the Big Bang itself. A theory that certainly could explain cosmic background wave and the red shift of the expanding universe, and even satisfies religious claims of things like God making everything. Everything is completely all right until we step beyond the beginning. People have asked numerous questions, “What was there before Big Bang?” The scientific community with a Godly authority turned all of these questions down. I will not repeat them.

But this was not all. This theory at last seems to be breathing it’s last (and thank God). The theory, which was once rejected, is now betting a rebirth – The Oscillating Universe theory. The General Theory of relativity, which so well explains everything regarding gravity, fails miserably in what we call Singularity – space and time condensing to one point – densities touching incredible values and distances reducing to about 10^-39 - the plank scale. And the reason? The same thing, which my dear blogmate Arun and I have been arguing upon – Calculus. We all know that charge is quantized, so is angular momentum of electrons, even mass. Let us take a step forward and extend quantization to time and space. Space is nothing but a fabric woven out of individual fibres. Calculus cannot be directly applied over discontinuous space. However applying it with a little modification allows us to end all problems. This theory is popularly known as the Loop Gravity Theory and interestingly but as expected originated in India.

The Theory was aimed at explaining the physics at plank scale which it did successfully. However, it led to another implication and directly counters the concept of the Big bang.. When all matter in the universe approach singularity, the theory says, there comes into play a force – one of tremendous magnitude, manifold greater than gravity itself and repulsive in nature. The situation is similar to a ball hitting a spring and bouncing back.

Certainly with this knowledge we can answer the most controversial question, “What was there before the big bang?” The answer is there was the countdown to a big crunch. We now have a universe that does not begin at the big bang, but only is symmetric about it.

What I want to say is here – Wasn’t it Obvious? We should have guessed it earlier. Let me explain why and how.

I would like to repeat the philosophy of a 2^nd century Chinese philosopher. Every event is preceded by another event. (The former is the cause of the later) Hence, the implication follows that there has to be some thing before the Big bang the cause of the Big bang, more specifically. (Speaking further, we can say that there should be no beginning to the universe, but we will see to that later) To further justify the statement, and denounce the creation of space-time at t=zero (and with it the Big bang theory), I will give the following argument.

Let us say there was a primeval atom, which exploded to create the universe, space and time. The question is why at all did it explode? This can be answered in two ways. Firstly there was some thing (or someone …say God) outside it who/which caused the Big bang to happen. That means, there was something – matter, energy or say a consciousness excluded from the Primeval atom. But this is against our Big bang theory. The second way is to use probabilistic mechanics. The primeval atom just like a radioactive atom had a probability of disintegration at any given time. (I am sorry, but using probability without the concept of time is just impossible.) So there has to be Time before Big Bang. This again violates the Big Bang theory.

I would love to write more but its not possible in a single blog. I will put it all in the second part very soon. So stay tuned, the sting is in the end, I assure you.

Saurya "Time" Mishra

The Great Relativity bomb plot

Hi !!!
This is a comic strip based on the theory of relativity. Click on the links to see the pics.

When Albert Einstein advanced his special theory of relativity in 1905, he turned upside down everything that common sense and science had established about time. He said that time is not absolute, but is a relative quantity that could show one value to one observer while seeming different to a second viewer. The whole thing seemed preposterous.

Though most scientists came to accept the Einstein theory, its principles have continued to elude many of the less informed - including, to his lasting regret, the villainous felow at right. He is the sly and ruthless Agent X, an international comic - strip spy who is plotting a daring act of sabotage aboard the most fantastic train in the universe-the Relativity Express. The Express travels at a speed approaching that of light. At this velocity the extraordinary effects of relativity are apparent. Objects shrink in length. Past, present and future become wildly mixed. Moving clocks do not remain synchronized with those standing still; even man himself ages less rapidly. Such astonishing events will cause the downfall of Agent X. Shrewd and cunning he may be, but like all criminals he has committed a fatal error: he has failed to keep himself informed about the odd effects of relativity.

---

1. The notorious Agent X, beady eyes hidden behind dark glasses, gestures toward the sleek Relativity Express, the train that is to carry forward his fiendish plot to blow up the world's greatest nuclear power plant. Hidden aboard the express is a bomb, carefully timed to go off as the train passes the plant. At that moment the express will be traveling at its top speed of 140,000 miles per second, three quarters the speed of light. X is confident. He has calculated well and is certain his plot will succeed. But he is in for surprises!

---

2. "Everything depends on time," muses X as he sneakily watches the loading of an extremely accurate clock on the Relativity Express. The clock is the key to his dastardly scheme. Inside the clock Agent X has planted his bomb, set to explode when the hands point to 1:30, the very moment the train is scheduled to pass the nuclear power plant. Only this precise clock and this dependable train can achieve X's evil purpose-if either the clock or the train runs just one second slow, the bomb will go off 140,000 miles past target!

---

3. Agent X has prepared a map of the bomb plot. He knows that the train clock is due to be set in accordance with the giant master clock near the track; this, he assumes, will insure his bomb of split - second accuracy. Just to be sure, however, he plans to check the train clock once again as it passes the steeple clock near the power plant. Meanwhile, his lookout will be watching for the train; once it passes he will proceed in his jet powered getaway car to a meeting with X at the overpass-as the Express roars toward its rendezvous with doom.

---

4. "On time!" gloats the cunning agent as the Relativity Express passes by the master clock, at the very moment it sends a noontime signal to synchronize the train clock. Now the bomb must be correctly timed, thinks X smugly, proud of his wicked plot. But little does he reckon with the effect of relativity on time at the train's great speed. The strange shape of the clock tower offers a clue, but in his exultation Agent X fails to notice. The wily spy will suffer severly for his ignorance; he is about to learn about relativity the hard way.

---

5. But suddenly X sees that something strange is happening! The lookout is a broad-shouldered, heavyset man - but this fellow standing at trackside is incredibly skinny. What's more, the bench and even the trees are peculiar, pressed into narrow shapes. Only the recognition of a hand radio like the one that controls the getaway car indicates to X that this might be his accomplice. He waves frantically at the man as prearranged but he is not sure this is the right chap. His first encounter with relativity has shaken him badly.

---

6. The lookout, who is really as squat and sinister as Agent X remembers him, is equally stunned by what he sees. He was told the train would be streamlined - but instead it is like a string of squashed - up streetcars. And look-oval wheels! He, too, does not know that relativity makes an object shorter when observed in motion. At last the lookout spots a distorted man waving madly from the rear car. Shaking his head, he prepares to follow in the getaway car. He is not sure who the fellow is, but he proceeds on the hunch that it is his leader, Agent X.

---

7. Beset by doubts, Agent X turns again to his map for reassurance. The next landmark is the town with the steeple clock. "I'll check the clock on the train one last time when we pass that accurate steeple clock," he mutters. "If the two clocks agree-and why shouldn't they?-the bomb will be perfectly timed and the plan will succeed. Then I'll drop off the train." But now the once-cocky undercover man is gripped by fear. What could have made the lookout seem so unfamiliar? Something outlandish is interfering with the plot!

---

8. The first real evidence that something has indeed gone wrong is spotted by an innocent bystander, a little old lady passing near the steeple clock as the Relativity Express speeds by. The train is actually moving so fast that only in a comic book would it be visible, but the sharp- eyed little old lady can read the clock; it says 12:40. "How odd!" she remarks. "The steeple clock says 1:00 and it's been right ever since I was a little girl. The funny clock on the train must be slow!"

---

9. At the same moment Agent X spots the steeple clock, leaps from his seat in disbelief and rushes to the car door to check the clock on the flatcar. Sure enough, it says 12:40, although the steeple clock reads 1:00. "Ye gods!" he shouts. " That steeple clock must be wrong! It must be fast- or else it was set wrong! I know the train clock was correct back at the master time station." The whole plan is in danger! In near- panic, X looks for the conductor to tell him that the world has gone mad; the clocks are all wrong.

---

10. "Both clocks are right," smiles the knowledgeable conductor. "But each clock is running slow relative to the other. As you can see, the steeple clock, which is moving relative to us, has a second hand that ticks more slowly than the second hand of our train clock. But it depends on where you stand: the people on the ground see our second hand as ticking slowly. Furthermore, the steeple clock and the master clock were never really synchronized from our point of view- although they were from the viewpoint of someone on the ground."

---

11. There is only one hope for the desperate Agent X now: he must reset the terrible bomb to take into account the time change caused by relativity. He has tricked the conductor into telling him that they will pass the power plant when the train clock says 1:00. Now Agent X must change the bomb mechanism to explode then. He slips from the coach onto the flatcar bearing the clock. If he can only reach the clock without rousing the drowsy guard, he may win his battle with relativity after all.

---

12. Agent X creeps up to the clock stand, against which the guard is resting, slowly opens the door and reaches inside for the bomb. The seconds tick by as Agent X tries to adjust the bomb mechanism. But the noise of Agent X at work nearby awakens the guard, who leeps to his feet. Agent X hastily abandons his work and jumps to the top of the coach to try to make his escape. "Rats!" spits out the evil villian. "The plot is a failure; I must flee before all is lost." But the guard hangs onto his coattails.

---

13. As Agent X doffs his coat he shows he is well prepared: strapped to his back are rockets capable of propelling him at half the speed of light. Away he zooms! "Success!" he exults. "Since the train is traveling at three quarters the velocity of light, I must be going at one and one quarter times the speed of light- enough to escape any gunfire!" But if X really understood relativity he would know that no object can attain the speed of light, much less surpass it. X is going at ten elevenths the speed of light- and that will make a difference!

---

14. A railway guard with the eyes of an eagle notices the commotion on top of the crack Relativity Express. Since anything can happen in a comic strip, he is able to race up the overpass before the train, which is zipping along at 140,000 miles per second, passes by. His laser pistol is in his hand. With this weapon he will be ready to fire rays that travel at the speed of light when the train and its would-be saboteur pass beneath him. The relativity-crossed Agent X does not know it yet, but he is about to pay dearly for his wicked ways.

---

15. As Agent X rockets over the roofs of the Relativity Express, he is the target of both guards. At the instant the two guards come abrest they fire their laser pistols. The gun on the train is moving, the other is stationary on the overpass, but- because the speed of light is always the same regardless of the motion of its source- both laser beams reach their quarry simultaneously. The hapless X, receiving his harshest lesson in relativity, is struck not once but twice.

---

16. The great nuclear power plant is saved as the Relativity Express grinds to an unscheduled stop. After frantically searching the clock, a guard finds the bomb, disarms it, and holds it aloft jubilantly. "The bomb," he exults, "was set for 1:30 but it is only 1:00 on the Relativity Express now, for the train clock has been running slow relative to the ground. Thank Heavens for relativity; it has bested the evil Agent X." Meanwhile the benighted agent is stretched out on the ground behind him.

---

17. Foiled by relativity, the once-smug Agent X is hauled away. The train, stopped, measures exactly the distance between two telephone poles; at full speed it was compressed to a fraction of that space (8); its wheels are round once more. A guard says pityingly, "Don't take it so hard, X. There's solace for you. Since everything on the train happened slowly relative to the ground, you're actually half an hour younger than you would have been if you hadn't ridden the Express." And so, younger but wiser, X is dragged off to jail.

Want to know more about relativity?
Click Here.

ENTROPY has INCREASED AGAIN

HEY BLOGMATES !!!

& Heyy Arun...
Your previous comment appeals to me big time for I'll share something with ya pal ! Even as I write this, therez a thought in my brain telling me to do it with adibatic & reversible processes as far as possible so that there is least increase in the entropy of the universe. When I walk, I think of taking the shortest route possible only because I don't want entropy to increase. Only that I realized it sometime last year that thinking to conserve entropy, I was infact increasing it ! The entropy I saved walking a hypotenuse-cut through a park was little compared to the effort I spent thinking about it. The heat released in my brain, the possible disorders etc etc.
Today it occurs it me, whether it was of any use ? Is entropy actually that bad ? Infact is a broken glass any worse than a not-so-broken one ? Well, science discusses the objectivity of a problem but what decides its subjectivity ?
Infact whats the definition of wrong & right ?
NOW ... thats too many questions at once ! That too very much varied.

Well. Okay. what about "" DISORDER "". Thats what ENTROPY if a degree of. But if ""DISORDER"" really that objective ? Or mayb we can define DISORDER in terms of entropy. Well, then is an act of murder a disorder or order ?
Im sure this is not a question answerable by science. Nor does science intend to adress such queries. But wat about them ?
I have a little piece of writing on entropy that I'll shortly post, something that I wrote an year back.

As for H U P , hmm... even I went through the same thoughts once! Though its intriguing to know that waves of particlas are considered to be waves only because there is to means to look into the wave !
Infact the de-Broglie thingy is pretty much the same thing as the HUP... just 2 ways to say the same thing. The same thing being that weather we say that there exists a particle which is smeared across a region in space, or there's a wave not a particle which is present, its the same thing !

Indeed theres a lot of similarity in our thinking Arun ... hmmm

Newayz.

Will try & be regular with some posts !




TWISH
PS: Sry Gawd for all this increase in entropy...

I Hate Capacitors

Hi guys,
Some thing has been eating me for days. Its about capacitors and may sound trivial but I wil assure u it is not so. The question is: "what will be the capacitance of a parallel plate plate capacitor when it is filled with a conductor touching both plates."
All books I have seen so far say it will be infinite or tends to infinity, but i dont agree. I will put my view point.

let us go to the grassroots and define capacitance. The ability of a capacitor(or any object for that matter) to 'store' charge at a given pottential difference. Now once both the plates are connected the whole assembly is nothing but a conductor. Two statements here:
(i) Any conductor except a superconductor has some resistance, no matter how small, it is non zero. Thus there will be some pottential drop. V not= 0
(ii) No part of a conductor can accumulate any net charge, because of the presence of charge carriers (electrons). Q = 0
Thus the capacitance C = Q/V = 0/non zero = 0

Now some thing very very absurd(funny rather) is written in one of the books (Arihant Electricity and magnetism). It say since a conductor can allow infinite amount of charge 'though' its plates, Q>>>>V. So C tends to infinity. Wah bhai !! Listen to my analogy. Take a bucket, cut off its bottom and say u have a bucket of infinite capacity !! LOL !!

Intrestingly and disgustingly nearly all physics trachers disagree with me. i am the lone fighter for my cause. I have ddecided to conduct an extensive experiment on this starting from 25 Sept after the FIITJEE exam ;) So what do you people think? Am I wrong ?

Saurya Time

HaPpY InDePeNdEnCe DaY!!

Just a filler post - to remember those who made it possible for us to celebrate
The 60th Independence Day of India.

          JAI H
           JAI HIN JA   JAI
            JAI HIND JAI HI
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       JAI HIND JAI HIND JAI H                 J         JAI HIND J
   JAI HIND JAI HIND JAI HIND JAI              JA     JAI HIND JAI
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   JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND JAI HIN
    JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND J JAI HIND JAI
    JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND  JAI HIND JAI
JAI HI JAI HIND JAI HIND JAI HIND JAI HIND JAI HIN        JAI HI
JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND      JAI H
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JAI HIND JAI HIND JAI HIND JAI HIND JAI HIND JAI HIN        J
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         JAI HIND JAI HIND JAI HIND
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          JAI HIND JAI HIND JAI HI
           JAI HIND JAI HIND JA
           JAI HIND JAI HIND J
            JAI HIND JAI HIN
             JAI HIND JAI HIN
             JAI HIND JAI HI
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                    JAI


Incase you have time, do see this:    
[Link to Flash Movie]

--
Gr81
I aM PrOuD To Be An InDiAn!

Time is back ...

Okay okay,

i know ... u all r really relieved 2 c me at last. I was hell busy ... working on ambigrams (thanks to Mr Dan Brown), mirror writings(Da Vinci Inspration), flute playing(sparekh bhai zindabad- great flute player), trying (hoplessly) 2 solve the Reimann hypothesis, experimenting on 'conductor mediated variable capacitance',blah blah blah ...

Now the purpose of this blog... i have got two things to post ... tell me what i should post first
Theoritical analysis of 4th analysis (my original and first research work) or Ambigrams and illusions(i love it!)

Time is back (may vanish again)

The Chaos Game

Here's about a lovely game I've been playing for the past week or so (it really screwed up my study schedule). It is just one of the pinnacles of the beauty of random processess. I hope you know I'm not talking about a computer game or sport.

I'll describe the basic process of the game now. It's very simple. Take a number of points (generally start with three, you can't do more without a program) on a piece of paper. Now supposing you've taken three (I'll assume you can all generalise it) points, considered vertices (A, B, C). Actually, these vertices need not be in ANY regular conformation. But again for aesthetic sense, consider them in an equilateral triangle. So you have three points in an equilateral triangle on a sheet of paper.

Now mark a point anywhere you like, inside the triangle, outside (even at infinity, but thats a wee bit impractical). This is your initial point, technically a seed. It really doesn't matter where its taken. Take a die (or create a random no. program). Assign two numbers to a vertex (if its a good die, which we assume it is, each no. has equally probability, so it doesn't at all matter). Suppose the following assigniations: A = (1,2) B = (3,4) C = (5,6). Roll the die, and mark your next point at the mid-point of your original point and the vertex indicated by the die. Roll the die again, and using the new pt. generate another pt. Continue doing it ad-infinitum (or till you go mad).
For example, let your initial pt be S. You roll a 4, then, mark X1 at the midpt of SB. Roll again, and get 3. X2 = midpt. of X1B. Roll:1. Mark X3 = midpt. X2A. Go on and on.

Honestly tell me what kind of figure would expect from such a random process. Some would say a filled triangle, and fewer a random figure that doesn't quite cover the entire triangle.

Time for some pictures eh?
Here is the plot for the above:
1. Plotted with just 10 points. No structure is inherent:

2. Plotted with 100 points. Some structure visible:

3.Plotted with 1000 points. Structure is glaringly obvious:

Just goes to show that the human intuition is extremely biased on its experiences. I've read two books about chaos, and a good portion goes in droning about how we've accustomed our minds to complex stuff can be achieved only by complex processes, and random processes bring out random results. The above figures tend to form the Serpienski Gasket, which is a figure that can easily be drawn through the process: Take a triangle, and exclude the triangle formed by joining the midpt of the sides. Do it for every single triangle you get. This is and example of a figure with INFINITE length but ZERO area. Another feature is that the figure is infinitely detailed, which means that it never lands onto the same spot, and no matter how deep you go into the figure, you will still see detail which is microscopic at that scale. It is also absolutely self-similar.

Either way, to extend the figures, we can take the points as 4,5,6, etc. (4 it comes out doesn't show anything, its and exception). We can also change the recursion to give:
X2 = (Vertex + X1)/R, where R is the ratio. Here we've taken R to be 2, and got the midpt. For different R, it doesn't exactly give us that.

So here are some more interesting pictures:

1) The same triangle, in much better detail (10^5 with a bettter plotter LabPlot, also freeware):
2) A skew triangle, just to show you the lack of need for regularity:
3) A hexagon with ratio 3. This is undoubtedly the most beautiful thing I've created (I don't draw very well):
Just some more notes, the figure in the center is a Koch Curve, which to people who've read it is an amazing revalation, because of the amazing shape that it is. Just to tell you, take an equilateral triangle. Take the middle third of each side, and split it open into two parts to form an equilateral triangle with the side = 1/3 of the base length. __ becomes _/\_, with better ratios of course. Keep on doing this. It gives you finite area, but infinite length.

Ok. One last note: You really should try to experiment with this. You'll come across a lot of interesting, and semi-obvious realizations. For example, by changing the ratio R to 3 for the triangle, you'll get a similar triangle figure but each triangle will be a bit spaced. If you do the hexagon, with a ratio of 2 instead, you won't be able to make up much. Extrapolating ,the ratio gives how far apart they are, with too small a ratio, they'll overlap and you can't make out anything.
For further reference:
MathWorld: http://mathworld.wolfram.com/ChaosGame.html

Some graphs for sparekh

I thought I'd plot the graphs that sparekh wanted (I was feeling pretty jobless at the time, despite a lot of work). I basically wrote a program (in Python, in case anyone cares) and used gnuplot (debateably to most powerful free plotting utility) to create the images.

-> This is the graph for N = 100


This is the graph whe N = 1000 ->

... Thinking about Thinking ...

Heyy Bloggies !!!

Oh I can't explain how my fingers are tickling to get busy typing an elaborate essay on a few really interesting topics I have in mind. But sorry for the dissappointment oh little fingers for due to lack of both time and patience, and a couple of exams on my head ( Skool + Coaching ), I'll have to part, with just a few words to say !

Arun and Ankit ! Welcome to our blog ! Arun, the post you wrote about what we are taught ( and what we are not... ) was nothing but true and I just can't help agreeing with it. In a way, I think you exressed a common feeling among all of us. But maybe they don't teach us how to solve the likes of Schrodinger Equation for two reasons that I can think of... firstly, to teach you need to get to know it yourself first ! And secondly, lets be honest here, how many 'general' kids around, do you think, would take much interest to actually learn to solve equations about quantum orbitals ?

Not to discuss the cons, lets think of the pros. Why don't we try learning the stuff we want to ourselves ? And I think this very blog would be a great medium or platform ! So any1 knowing howto solve second degree differentials with a couple of wierd vector calculus symbols in it, plz come up and help ! hehe kiddin lol.

Other than that. I'd like to share a thought. Let me clarify my stand by pre-rationalizing that what I'm going to say isn't SCIENCE for there aren't many things you can proove by experiment about it. Its something common to all of us though, whether we notice it or not. What would you people say about conciousness ? The very thing that gives us this unique ability to question the very laws of GOD ? How can you expalin something like it interms of Physics ? The very entity which keeps us thinking. Which makes us slaves of Time's direction ( not YOU Time ;-) ! ).
I think it has more to do with the laws of nature for in a sense, it is the very genesis of any experimental result ! If conciousness didn't exist ? Would this universe exist ? Or would it matter if it existed ? Or leave alone that, would things like the Uncertainity Principle still exist ?

Sumhow I have this intution that our conciousness, our power to think independantly, is not something which runs by natures laws ! It creates them ! It is the very creator of or universe, and sumhow in the backdrop, every conciousness is related.
I have this instinct that finding the mysterious nature of our conciousness would be a very major step to understand the nature of or create or discover a complete theory of everything !

I have my reasons for thinking so. I can share them, but for that, sometime later.
Till them you guyz n gals can wonder how you CAN wonder ...

Me Take Leave,

May KVamPYs Rule

~ Twish ~

Where Are We Going?

I've slowly gained an immense (I can't encompass it) disdain for our academic syllabus. I'm preparing of the IIT's (as ya'll should know), but I still feel that lack of true persuance of the holy grail of knowledge. As a gentle warning, this is going to be a ranting post, so pardon me if any emotions are flared.

The main problem I have with what we are learning is: WHAT ARE WE DOING WITH IT??? Do we analyse, rip apart and reconstruct situations. What makes a parabola a parabola? There are like a thousand questions which give a very interesting results, GENERAL results. Why don't we deconstruct the situations and understand WHY things happen? I'll give a simple and not very good example: If you find the locus of points from a pair of tangents are drawn to a parabola, such that the intercept made by the pair of tangents on ANY line parallel to the directrix is a constant, it ends up being a parabola PARALLEL to the first one.

Especially in maths, we tend to take a lot of things for granted, that two parallel lines must be straight. If we analyse (which we don't) non-eucledian geometry we see that this is not a condition. We take so many things for granted, that when it comes to interesting new worlds (which represent our world better) we make those same wrong assumptions.

Physics too is becoming a bore. I love physics, and it is my forte, but we take a lot of things for granted again. We derive results for very simple cases, and push them off as universal things. We make horribly inaccurate simplifications of certain differentials. For example the expansion of a rod equation, (L_f = L_o (1+aT), the T is valid only for very small degree changes, in the order of 10^-5 to yield any degree of accuracy, but we use it for things with 40-50 degree differences.

Chemistry is the worst of them all. We were shown Heisenberg's uncertainty princple, without actually understanding WHY it is INESCAPABLE. And Schrodinger's Wave Equation is nothing but a jumble of symbols (though elegant and very professionalistically complex symbols). We are told that it is one of the most important equations there is, and that it can tell the electron density. But WHY? Leave why, how do we apply it? We surely haven't used it ever.
Organic chemistry is a funky subject, because a lot of things are not really known. But I know for a fact that there are good and consistent explanations for most things that we do. But most of the time we have so many exceptions and we have to consider simple rules of thumb: If the product is complex, it is right. If the probable yield of the compound is fractional, it is probably right (I've kinda made these, and they work well).

Why can't we leave this stuff behind? We are in our 12th, and that is definately old enough to understand what's going on. We should understand this world better, and most of what were doing doesn't push us in that direction. No matter what we do, we will have to analyse situations break them down, and there no time too soon. I don't know if it's just me going through these emotions, but knowing that most of you are scientifically orientated, I'm sure that you understand what I'm going through.

Little time, lots of confusion

Let me clarify a few things first up. I am Ankit Sagwal,one of the guys from Dps Rk puram and not the immensly popular ankit pandey(by the way, where is he? still not found the time to join).I will post my photo as soon as i figure out how to do it(maybe that would work). I have not gone through the blog yet(its a lot of text) but i'll surely do it.
I think this space is meant for something more interesting rather than a general talk. Ok lets give you one of my favourites:-

The task is to fill 1cm diameter spheres into a box(cube) of 10cm edge.find the best pattern as well as the maximum possible no.

Short and smart!!

the next few lines might act as an apetizer for u guys(and gals-i can see a lot of them on the list). The question is not as easy as some of the first timers might think. Others might have done the 2d version of it(i should have given that first-comparetively easier)

a square of side 10cm is to be filled with circles of 1cm diameter. find the maximum no.

hint:- slightly more than 100

I think this should be it.Think over it.

Maths has always been a treasure (this is one of the gems)
I've got to rush, make my substitutions in the timesdreamteam(i wonder how many kvpyians know about it(fantasy game of football similar to super selector)) and then get down to study for my maths exam tomorrow(oh!! i have to start taking school exams more seriously).
byeoo

Posted by ANKIT SAGWAL

Miss you Blog !

Hey Blogmates & Readers.

This is Twish. For those who're new to this blog, just check out my intro in the archive. Im the admin of this blog though I've been so much out of touch with it.

Looking at it today, I must say Rash has been talking alot of pains adding new things to the page! Its a great job ou've done man!

A welcome to so many of the new members! I can see a couple of friendz who went to IISc as well ! Isnt it a great idea to spread out blog link to them as well... ! At last we all deserve the KVamPY title! Watsay Arun...

Time, nice generator man. Though I think that picture you've posted is miserable similar to the one I sent you about my generator ! I think I deserved a mention for the help yaar ! hehehe newayz...

Sry pals, for not posting. Not blogging. Been busy. Though the new ones ...
DO CHECK OUT THE DEAD ENDS SERIES OF POSTS IN THE ARCHIVE ! IM SURE ULL FIND IT INTERESTING.

Take Care PPl !

MAY KVAMPYS RULE

~ || Twish || ~

hello

Hi guys. This is Ankit
I guess i am a little late in joining.

It's the IISc kid

Hey,
I saw somebody ask for my intro, so I'll start off with that. My name is Arun Tejasvi Chaganty (call me arun), and I'm studying in 12th (along with most guys here i think), in FIITJEE (curses, lighting and gasps). Very very luckily, this place isn't as coaching centre-ish as i feared it would be, and I still have time for my on stuff (more like i don't really care for their work (not after the summer camp atleast)). As you would have seen, I like nested brackets a lot, so I'm sorry if that causes inconvinience to any one. I joined KVPY this very year, and along with most of the people down south (I'm located in Hyderabad), we got to go to the IISC campus.

I think this part is what more people are interested in, so I'll elaborate quite a bit. All the SP, SB and south-zone SA students had their centre in IISc. Please pardon me to mention that IISc is THE most prestigious campus in India (I don't think anyone can object here), and basically I'd like to rub that in your face. The only way you'll be able to counter is if you post a review of the campus where you went (This is an elaborate ploy to get you to do the same).

Ok the fact that there were students of varying graduation levels was good in a sense, and bad too. In most of the labs we visited, the explanations were never very satisfying for both of us at the same time. On the other hand, these guys are really great guys to interact with (not all of them, but a lot of them). A large number were from the IIT's and BITS.

I'll kind of give an overview of what we did. We mainly attended a lot of great (and a few not so great) lectures by great professors. These lectures were mainly on common ground, topics that were entirely out of stream so that both the SA and the SB+SP guys could understand whats going on. I'll give a list later. Then we had a lot of lab visits. We saw a lot, but I can't say we did too much. It was interesting, and exciting at times, but it's rather inconvinient when you have like 20 people stuffed into a small room with a lot of expensive equipment (You won't believe how seemingly disorganised some of the breakthrough research labs are). That was pretty much it. We were allowed to roam around the campus at our free will, and visit the library (heaven on earth).

The campus was just beautiful. Perhaps it was the real heaven, and the library was just a teaser. Either way, there were a lot of trees, and a lot of crows, and a lot of white patches on the roads (I hope you can put 2 and 2 together). The wild life and greener there made it a great place for the ecologists there, who were doing some really interesting experiments with social bug behaviour. A group also actively worked in a nearby (or not so nearby I haven't a clue), national park monitoring elephant populations and battling poaching. There was a huge library, a lot of departments and a supercomputing research lab (obviously the low of our lab visits. They can't show you much more than a LOT of computer terminals), an NMR research centre, a nano-research lab, and a cryogenics facilities. THe other high end equipment was in the departments. A bunch of spectrometers, sputtering devices, atomic force microscopes, electron microscopes, blah blah blah (the average guy would be watering by about now, but I'm sure youa'll have see this stuff too).

We were also taken to the Raman Research Institute, which is another amazing place. The most remarkable thing there was the laser-cooling lab, where they slow down electrons to nanoK temperatures. I'd suggest you read this stuff up.
As I said I'll list most of the lectures (everything I can recall):

Evolution of Social Behaviour: Do we form social groups just to ensure our genetic make up goes on? This professor (Prof. Nanjudaih V) was just brilliant, and mentioned quite somethings about chaos theory also.

The Many Forms of Carbon: As you guessed, it was lame lecture. The plus point was that the lecturer presented a new form of carbon which was researched in the campus: Super Carbon: an conducting amorphous form of carbon. It was interesting in how it was made using logical assumptions (better than fullerene which was a fluke)

Protiens and how the Work: A great lecture, though highly technical about how protiens are made.

Chemisty in Life: About how molecules work in life (to a lesser degree). It wasn't a very enlightening lecture, but the lecturer:Prof. Uday Maitra, was just mindblowingly good, so I guess we all fell in love with him, rather than what he was teaching

***Black Holes: This was undoubtedly the BEST lecture I've EVER EVER had (which isn't many, but still) by a professor from the Raman Research Institute, Prof. Srinivasan G. It explained in a very good technical manner about black holes. Great lecture again

Variations from the DNA Helix: A good lecture, but perhaps not great

Colours In Chemistry: Interesting demonstrations showing different reactions producing flourescent colours, interesting colours blah blah.

Virtual Experiments: Again by Prof. Uday Maitra. He showed a number of experiments performed somewhere else recorded on "tape" (nobody uses tape anymore). He did a good walkthrough through all the experiements. Again most amazing professor I've seen.

There were four more lectures which I missed because of a 103 degree fever (weeping hesterically). I wish I could have attended them, but bad luck I guess. I'll just have to pray that somebody posts a good explaination of these lectures. (they were the last four lectures).

Now if you haven't gotten sick of me, and the length of my post, I'll continue, but as I know that's not the case. Beam me up scotty (Star Trek anyone?)

Arun

FROM JUNK TO VAN DE GRAFF GENERATOR

Ciao everybody,
This was my new project (more of a fun than a project)… I have made a van de graaf high voltage generator out of junk. Total expenses u wont believe it … Rs 25/- and a few costly hours of mine.
As u fellows know better that a van de graaf gen generates a very high voltage of the order of few millions. Just refer an NCERT class 12 book and u have a very nice topic on it. The major change that I have done is that I have used ‘theiboelectric’ effect instead of a high-tension battery.

We have certain materials that lose electrons readily and some that gain them easily. Here they are glass and rubber and plastic. I will not bore u with my worthless writings u see the pictures and comprehend likewise. I was helped by one of my local friend ... Avinandan rout. He is as talented as any of us only he could not make it to the KVPYians. I will also attach a schematic diagram to help in the comprehension.
The gen takes a lot of time to charge fully but ur hair does stand up. I specially thank Mr. Samuel Q. Field 4 his help. The idea was his but I modified it in several ways to make it better.

The van de graff gen was presented in the ‘The Uranium camp 2006’.
Just tell me if u want a detailed description and I will do so. Also if u want 2 know more about the Uranium camp (and the fun: I would love to write about it) just tell me.

Saurya "Time"
(Time is back)

DEAD ENDS : Part III : Justified lies

Here I am !
Bored of 2=1s aren't ya'll ? Here are some more of classic lies, told in the most decieving manner !


(1) *** classic *** ( Some PHYSICS for a change )
There in the figure, we have a ladder leaning against the brown wall. Its length is l & the two ends are labelled as A & B. End B is pulled in the positive direction of the x-axis with a constant speed V. The velocity of end A in the downward direction is U ( variable ). x,y are the respective coordinates of the two ends.

x² + y² = l²

differentiating w.r.t. time we get :

2.x.∂ x/ ∂t + 2.y. ∂ y/ ∂t = 0

2.x.∂ x/ ∂t + 2.y. ∂ y/ ∂t = 0
2.x.V = - 2.y.U(x)
U(x) = - x .V/ y

Now, when ladder falls completely, and becomes flat, then y = 0 & x = l.

To calculate the veocity of end A when ladder just becomes flat, we put the values in equation for U(x) getting :

U ( l ) = - l.V/0 = - ∞

So the velocity of end A becomes infinite when the ladder becomes flat ? !

(2)
We are all aware of the theorem of Mathematical Induction. However, none would have seen its misuse. Here is one such misuse which is horribly difficult to disproove !!!

Statement to be verified is :

S(n) : In any set of n people, all would have equal ages.

Now we proceed :

S(1) is true ( Since in a group(set) of 1 person, all have equal age. )

Let S(k) be true.

Now ;

In a group(set) of (k+1) people, we make all possible sets of k people. In all these possible set of n people, S(k) would be true (as per assumption) and hence all people in each of the sets would have equal members. Now since all such possible sets would have members of the same age, this is only possible if all the members in the (k+1) member be equally aged. Therefore All people in the set of (k+1) people have equal ages.

Hence S(1) is TRUE & S(k+1) is TRUE whenever S(k) is TRUE.

Hence prooved by mathematical induction , the TRUTH of statement S(n) for all n belonging to N.

Application of the above theorem for the set of BLOG MEMBERS "B" We conclude that All members of this blog are of equal age.
QED

(3) *** classic ***

ABCD is a square. BE = BC.
PQ bisects CD,AB.
OR is perp.bisect. of DE.
PQ, RO intersect at O.
∠ ABE is an OBTUSE ANGLE. ( clearly )

Δ ORD ≡ Δ ORE (SAS)
:. OD = OE

Δ OQA ≡ Δ OQB (SAS)
:. OA = OB & ∠ OAB = ∠ OBA

Δ OAD ≡ Δ OBE (SSS)
:. ∠ OAD = ∠ OBE
∠ ABE = ∠ OBE - ∠ OBA
= ∠ OAD -∠ OAB

But ∠ OAB - ∠ OAB
= 90 °

:. ∠ ABE = 90 °
However, we've assumed the angle to be obtuse. :. Every obtuse angle is a right angle. Similarly, It can be shown that every acute angle is a right angle.
QED

---

This is part III and I'll let ya'll know that 3's my lucky number. So hereby, I quit with this series. Not that the resources are over ! Infact they're endless. But today eve, I'm leaving for Delhi & I won't be able to be online so regularly. Though I'll surely stay in touch atleast twice a week !

A last message. I believe that us KVamPYs are special in some way. I also believe, that we can be a great strength when united ! So here's a request. Mayb you can't come online very often but do stay in touch by atleast going through the blog once a week !!!
This blog is for us KVamPYs, by us KVamPYs & of us KVamPYs.

So letz ROCK ... letz RULE !!!

& Ill borrow Rash's line...
SwItCh On Ur BuLbS !!!

~ Twishmay Shankar ~
( Twish ;-) )

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I HaVe ThE POWER!!

Well, does the title remind you of the classic “He-Man” Cartoon series?? Well I’m not posting about cartoons but this has to do with “Power.” But that’ll come later.

First of all, I wanted to post my intro too but was waiting for Twish to mail me the pics from the camp. So that’s me saying: ”I have the Power!!”. You want a formal Intro? Here you go:

Name: Rasagy Sharma (a.k.a. ‘Rash’ The Gr81)

Residing in: Delhi

Interests: Dramatics (Done loads of TV and Radio Shows), PlayingSoccer (Some of you who played with me know that – It’s a second religion for me!), of course anything to do with Computers (I just luv Computers!) and last but not the least, making Friends (and continuing the friendship too!)

Enough about me. So after reading Bravura’s post, I was sitting in front of my computer wondering about what went wrong there. Got some ideas, but couldn’t join them all up. And then a short chat with Twish only raised my ideas to higher powers… Yes. It was powers about which I have been thinking all night. Well, most of such weird looking problems arise from the fact that what we have been taught about powers, multiplication etc. is too basic (coz we were too young to understand complex nos. at that time). And even now, we haven’t updated our information about such elementary things, though we do know complex nos. etc. And thus arise such ques.

Well here are some examples:

1. 1⁰ = 2⁰

Then won’t 1 = 2 ?? (Say we have 2^x=2², then we say that x = 2, don’t we??!!)

2. To prove: 3 = 4
Proof:
Let a+b = c
4a-3a + 4b-3b = 4c-3c
:.4a+4b-4c=3a+3b-3c
:. 4*(a+b-c)=3*(a+b-c)
:. 3 = 4

Maybe most of you can find what’s wrong up there (I think you all Should find that out easily!). But ever wondered why even your computer’s scientific calculator can’t compute (-8)^1/3 ? Even though the answer is an obvious -2 ? (It says invalid input for the function: Got some clue??). Though its fine that it can't compute (-8)^1/2.

Another nice problem (which Twish told me during the camp) is the following:

We know that

4*4 = 4 + 4 + 4 + 4

:. 4*4= 4 + 4 +… 4 times.

:. x*x = x + x + … x times.

Differentiating,

2*x = 1 + 1 + 1 … x times.

:. 2*x = x

Hence 2 = 1!!!

All such problems arise because we forget our assumptions – the definitions of the functions – the domains of the functions and we tend to generalize a formula we learnt in junior classes here.

Now what I was thinking was this:

x = 1^1/3

Then x³ = 1. And we get the solutions for x. So as this n increases, the no. of solutions for x also increase (which is n itself).

But if n-> infinity , we get only one value for x = 1. (Actually here we can’t replace n by infinity as n-> infinity but n is not equal to infinity.)

Also,

2 ⁰ = 1
1 ⁰ = 1
0 ⁰ = ?

Well infact 0 ⁰ an indeterminate form. So we can treat it as an exception.

But what if n is a complex no.?? According to Twish, it’ll lead to infinite solutions for x. I reckon that’s what messes everything in Bravura’s problem. So can some body explain to me what’ll happen with complex powers? (Do we have any physical interpretation other than just saying Z = 2 ⁱ finding Z??)

Sorry for writing such a Llllllooooonnnngggg post, but I think it'll compensate for my absence in the coming few days when I'll go out of station. So I hope to find many posts by then (posts by members other than Twish's Dead Ends - come on others plz post!)

And before ending, a bit of cheerleading… (yeah I’m at least good at that!) U ppl are doing a gr8 job posting stuff, but do visit the blog regularly (Too busy studying huh?) And do give more ideas as to what more to add in the blog..

So SwItCh On YoUr FuSeD BuLbS!!

~RashTheGr81~

DEAD ENDS : Part II : Burning Reality

Hi Again
As promised, here is PART II ...
Bewarethough !!! I'd certainly say this one is more wierd, more interesting but still a LIE which has been imposed wrongly upon reality :

(1)
Every1 here knows the pretty little Binomial thorem going as :

(a+b)ⁿ = aⁿ + n*b*a^n-1 + ... + n*b^n-1*a + bⁿ

Observing we find that leaving the first and last term, all other terms are a multiple of n.

For some wierd results, let us put n = 0 ;

LHS = (a+b)⁰ = 1

RHS = a⁰ + 0 ... + 0 + b⁰

= 1 + 0 ... 0 + 1

= 2

:. since LHS = RHS

2 = 1

QED

(2)

Consider the integral :

I = ∫ 1/x ∂x

Intigrating by parts ;

I = ∫ 1*1/x ∂x

= x*(1/x) - ∫ x*(-1/x²) ∂x

= 1 + ∫ 1/x ∂x

= 1 + I

:. 0 = 1

or, 2 = 1

QED

(3) *** CLASSIC ***

Have a look at the figure. O is the origin. C is the centre of the circle. P a variable point (x,y).

t = OP ; R = CP ; a = OC

The equation of the circle would be:

x² + y² -2*a*x + a² - R²

Now, t² = x² + y²

Also putting P(x,y) in circles equation we get :

t² - 2*a*x + R² - a² = 0

:. t² = 2*a*x + R² - a²

2*∂t/ ∂ x = 2*a

Now for the point with minimum distance , The above expression equals 0.

For that to be possible, a = 0, that is O and C are the same points !

Hence Whenever O is not the center of the circle, there is no point on the circle from which the distant of O is maximum or minimum.

QED

There is still more to come. Before thinking about the faults, appreciate the beauty of these propositions, how decievingly they proove the unproovable !

This in not the end.

~ Twish ~

---

NOTE : Those having difficulty typing math visit this link for keyboard codes :

http://www.planetburrito.com/tb/alt_codes.html

This is Somani

Hi ,
This is Somani,
Call me by any other nickname you please(just inform me about it )
For identification 'The girl whose hair stood up due to shock' should be enough.

I AM

Hi Every1
I'm Sunita Panda from IIT Kharagpur campus
u might remember me as
-the girl who used to ask stupid questions during lectures.
-the self appointed guide at the science city (till my job was outsourced to 2 strangers)
I think that should be enough

DEAD ENDS : Part I : Spark to a Fire

Hey Blogmates !

The last post reminds me of something I've been doing for years! Something, which I was avoiding to put up here. But now I've lost all patience so here I begin with a series of posts, which to me atleast are damn interesting !!! I hope you all enjoy it...

(1)

- 20 = - 20

or, 25 - 45 = 16 - 36

or, 5² - 5*9 = 4² - 4*9

or, 5² - 5*9 + 81/4 = 4² - 4*9 + 89/4

or, (5 - 9/2)² = (4 - 9/2)²

or, (5 - 9/2) = (4 - 9/2)

or, 5 = 4

or, 2 = 1

QED

(2)

The very interesting infinitie series :

0 = 0 + 0 + 0 + 0 ...

For those who don't find it so interesting, follow me.

0 = ( 1 - 1 )
:. 0 = ( 1-1 ) + ( 1-1 ) + ( 1-1 ) ...

Now all of you would have paid attention in primary school when we were taught the associative law of addition.
Interestingly applying that here,

0 = ( 1-1 ) + ( 1-1 ) ...
or, 0 = 1 + (-1+1) + (-1+1) ...
or, o = 1 + 0 + 0 + 0 + 0 + ...
or, 0 = 1
or, 1 = 2

QED

(3)
- 1 = - 1
or, sqrt(-1) = sqrt(-1)
or, sqrt(-1/1) = sqrt(1/-1)
or, sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
or, i/1 = 1/i
or, i2 = 1
or, -1 = 1
or, 2 = 0
or, 1 = 0
or, 2 =1
QED

___________________________________________________________
This is not the end. Its only a beginning ! Stay tuned for more of 1=2 syndromes ;-)
And you thought 1 + 1 = 2 huh ?

~ TwIsTeR ~

Playin wid INtergals

Hey Pravar !

Your post indeed looks puzzling at first sight though its nomore a fallacy than saying both ±2 square to 4! Let me elaborate!

The integrity(literal, not mathematical) of the solutions can be checked by diffrentiating both to get the same result sinX.cosX so where lies the fault ?
Take the two solutions to integral (without the constants mind you... )

I₁= (-1/4) * (cos2X)
I₂ = (1/2) * (sin²X)

There you go pal with a little of simple maths ...

I₁

= (-1/4)*cos2X

= (-1/4)*[1 – 2sin2X] =

= (-1/4) + (1/2)*(sin²X)

= constant + I₂

So there ...
The two differ by just a constant!
No wonder they are integrals of the same expression!
It would be better (& correct) practice to insert the constants & then show the result but the catch remains the same...

BOTH THE RESULTS DIFFER BY A CONSTANT WHICH HAS NO EFFECT TO THE INTEGRATION !!!

~ TWISH ~

The Lion MUST be caught ?!?

Car pulls ( engine pulls rather ) with force F.
Car moves with constant velocity V.
:. Net force on car = 0
Force by dissipiative forces such as friction = -F.

Now ; P = δW/δt = δ(F.s)/δt = F.δs/δt
Now since velocity is always relative, δs/δt = u is always relative!

However, since there are two powers acting, one by friction & one by engine, & net F = 0 , the net power on car is 0. This is from ground frame.

If a cycle follows at velocity U, in frame of cycle, the cars velocity = V-U. It is wrong to say that cyclist would say the power delivered by engine is F.(V-U) because the cyclist finds the car not accelerating & hence he caculates the work done by engine to be 0. The cyclist has no direct means to find from his frame what the work done by the engine alone is. ( Cyclist can't measure F, the internal force )

Besides, whenever engine applies a POWER, it makes the car accelerate. And acceleration is independant of relative refrence frames.Both someone on the car and on the cycle would measure the same Acceleration & hence find out the engine's power ( in absence of dissipiative forces ).

To get my point, try to sit on a cycle & follow a car (running at constant velocity) & think of an experiment to determine the power of its engine! You can do so by guessing at its friction, but not directly! This is the key to the problem. Work done is relative.

Therez another realated interesting thought. WHEN WE CLIMB STAIRS UPSTAIRS OR DOWNSTAIRS, THE NET CHANGE IN POTENTIAL E IS THE SAME. THEN WHY DO WE GET TIRED WHILE CLIMBING UPSTAIRS TO A GRATER DEGREE ???

Watz ur Wattage ?

Herez a puzzle:

I hope every1 has seen those water sprinklers spraying water in a garden. Nice little things they are, for they rotate by themselves throwing water around! Its obvious that laws of momentum conservation are the secret behind the working of this interesting gadget. But here comes the catch. Imagine that water is not made to gush out of the sprinkler. Instead, it is dipped in a tank and by some means, water is made to flow inside it. There can be 2 such possibilities :

• The pressure outside is increased
• The pressure inside the pipe is decreased.

The question now is ... is water flows as shown in the figure, which way would the sprinkler rotate ? ( Aniclockwise or clockwise ? )

Plz don't post you answers here, email them to twishmay@gmail.com with a satisfactory explanation.

~ Twish ~