Favorite Equation: Quadratic Formula - Solving for X

[ranger]

I am the first to mention,
E=mc^2.

Thats my least favorite equation. I don't have use for it. I dislike it becuase it gave rise to atomic bombs and so on.

 

[robphy]

I am the first to mention,
E=mc^2.

Thats my least favorite equation. I don't have use for it. I dislike it becuase it gave rise to atomic bombs and so on.

This page "From E=mc² to the atomic bomb" (from Einstein Online, Max Planck Institute for Gravitational Physics)
http://www.einstein-online.info/en/spotlights/atombombe/index.html
has an enlightening discussion.
(I have no association with that site.)

 

[theperthvan]

If 1+1 doesn't equal 2, then the whole of maths EVER has been in vain.

 

[Gib Z]

Thank God Hilbert lobbied for the axiomization of mathematics and we have DEFINED 1+1 to equal 2 :)

 

[ssd]

Thats my least favorite equation. I don't have use for it. I dislike it becuase it gave rise to atomic bombs and so on.

For that matter, the person who invented 0, the person(s) invented calculus, laws of physics, quantum theory, Bose (for his statistic) ...every body and ennumerable men of pure math... and big number of elementory results of Physics, Math, Chemistry ... all are to be blamed for the atom bomb.

I like E=mc^2 not because of the fact that it gives rise to atom bombs... but because of the enormous talent, imagination and brain work behind the derivation of it and the scope of human knowledge to get extended (to have a true picture of universe) standing on shoulder of it (I mean relativity theory).

 

[theperthvan]

Thank God Hilbert lobbied for the axiomization of mathematics and we have DEFINED 1+1 to equal 2 :)

Yeah, it obviously does. But WHAT if it didn't?

 

[Gib Z]

I think you wanted to bold text with the IF...but well yea, if it didn't, we're screwed :)

 

[spacemonkey]

P(A|B) = \frac{P(B|A)P(A)}{P(B)}

 

[robert Ihnot]

fedora: Thats my least favorite equation. I don't have use for it. I dislike it becuase it gave rise to atomic bombs and so on.

E=MC^2, I am not sure it had much to do with the atomic bomb. Einstein at first called it only a "theoretical" value, but later wrote a letter to Pres. Roosevelt because the Germans had split the uranium atom in 1938. Under Hitler the Nazis were very skeptical of anything Einstein did, but were seeking to build the bomb.

It certainly was known that some things were radioactive. Then we have the energy of the sun. A really important discovery was the possibility of a chain reaction on Dec 2, 1942 by Enrico Fermi at University of Chicago. For the bomb, we need a chain reaction.

Einstein, you know, was no engineer and did not build things. Some have said his greatest contribution to the atomic bomb was, along with Szilard, his letter to President Roosevelt. As for a chain reaction, Einstein is quoted by Szilard as saying, "It never occurred to me." http://www.doug-long.com/einstein.htm

 

[d_leet]

If 1+1 doesn't equal 2, then the whole of maths EVER has been in vain.

Can I say, consider Z₂ (Z is the set of integers).

 

[Gib Z]

First Point- I don't get you d_leet...
Second Point - Z being the set of integers in an american thing isn't it? I've always seen it like that from the internet and stuff, but when my teacher did it he said it was J, i put my hand up and said it was noramlly Z wasn't it? He said its an american thing, so i wasn't totally incorrect, but that didn't stop my stupid class for laughing at me. They seem to think I am a pompus bigot who thinks I know everything, and they love to see me get something wrong. Hate it!

 

[ssd]

http://www.doug-long.com/einstein.htm

That is Einstein to me.

 

[d_leet]

First Point- I don't get you d_leet...

My point was more or less that there are algebraic system/structures(I'm not sure which would be the correct term) where 1+1 does not necessarily equal 2, well even this might be incorrect because in the group Z₂ 1+1 does at least belong to the equivalence class of 2.. namely [1]+[1]=[2]=[0], where [a] represents the equivalence class of a, and a relates b if and only if 2 divides a-b. I'm not completely sure of the correctness of any this at the moment because I'm tired and it still is fairly new to me so if anyone would care to make a correction please feel free, however, I believe my point still stands that there are algebraic systems where 1+1 is not necessarily equal to 2.

Second Point - Z being the set of integers in an american thing isn't it? I've always seen it like that from the internet and stuff, but when my teacher did it he said it was J, i put my hand up and said it was noramlly Z wasn't it? He said its an american thing, so i wasn't totally incorrect, but that didn't stop my stupid class for laughing at me. They seem to think I am a pompus bigot who thinks I know everything, and they love to see me get something wrong. Hate it!

I'm not sure about this, I've always seen it in textbooks as Z, but then again I live in America, and all the textbooks I have seen were written here as well, so i don't think I can really answer this one way or another.

 

[theperthvan]

I'm an Aussie and have only seen Z for the set of integers.

 

[Gib Z]

My teacher said all schools in New South Wales had J in the syllabuss and not Z.

Im guessing that you live in Western Australian, thePERTHvan, so maybe that's why.

 

[theperthvan]

Indeed I do

 

[Gib Z]

That post is 9 characters long! I thought PF has a minimum of 10 and that spaces don't count.

EDIT: I tried posting 10 spaces, didnt work.

 

[murshid_islam]

< 10

 

[uart]

My teacher said all schools in New South Wales had J in the syllabuss and not Z..

That's quite interesting GibZ. Personally I've only ever seen Z used but I have to admit that J seems a bit more intuitive. Still I'd prefer to have a standard (world wide) convention for it, whatever that standard happened to be.

 

[CRGreathouse]

I'm in the US and have seen J for integers, but only once and then only in high school. I've never read a paper from Australia that used anything other than Z for integers, and I've read maybe a dozen number theory papers from Australian authors.

 

[quasar987]

Z being the integers is certainly not just an american thing. And in fact it's primarily a german thing as Z is for 'Zahlen' (numbers). Before english, german was the official language of science and many words have their origin in german. For instance, what we call fields in english are 'Körper' in german, meaning "body" and the french word for field is 'corp', meaning "body" as well. 'Ring' is the litteral german translation of 'Zalhring', a term first coined by Hilbert according to Wiki.

An example from physics: the partition function, conventionally noted Z, stands for 'Zugstansum' (probably spelt wrong) meaning 'sum over all states'.

 

[Gib Z]

I want a stand world wide one too! I don't care, Z or J, though i think Z looks better in BlackBold :)

 

[PhilosophyofPhysics]

- \frac{\hbar^2}{2m}\nabla^2\Psi +V\Psi = i\hbar\frac{\partial\Psi}{\partial t}<br />

 

[Gib Z]

Nice. Very nice. You do Schrodinger proud.

 

[theperthvan]

Nice. Very nice. You do Schrodinger proud.

How can he be proud if he is dead?

 

[Gib Z]

>.<"

Have you observed him dead? Hes in a superposition of many states, one of them in which he is alive and proud! :P

 

[murshid_islam]

great answer, Gib Z.

 

[PhilosophyofPhysics]

e^{i\theta}=\cos\theta + i \sin\theta

This has already been mentioned but I thought it was the coolest thing ever when using series to show it.

 

[Plastic Photon]

Laplace L(f)=integral(e^(-sx))(f)dx

 

[Thrice]

Us physics guys chiming in

G_{\mu \nu}=T_{\mu\nu}

(screw the 8pi)

 

[Sir]

\int_{-\infty}^{+\infty} e^{-x^{2}} = \sqrt{\pi}

 

[robert Ihnot]

\frac{\pi^2}{6} = \sum_{n=1}^{\infty} \frac{1}{n^2}

\frac{\pi^4}{90} = \sum_{n=1}^{\infty} \frac{1}{n^4}

Discovered by Euler, who continued to study the Riemann Zeta-function,


\varsigma(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}

And, as uart tells us on page 1: \prod_{n=1}^\infty \frac{1}{1-(1/p_n)^a} = \sum_{n=1}^\infty 1/n^a

 

[AKG]

My point was more or less that there are algebraic system/structures(I'm not sure which would be the correct term) where 1+1 does not necessarily equal 2, well even this might be incorrect because in the group Z₂ 1+1 does at least belong to the equivalence class of 2.. namely [1]+[1]=[2]=[0], where [a] represents the equivalence class of a, and a relates b if and only if 2 divides a-b. I'm not completely sure of the correctness of any this at the moment because I'm tired and it still is fairly new to me so if anyone would care to make a correction please feel free, however, I believe my point still stands that there are algebraic systems where 1+1 is not necessarily equal to 2.

There are algebraic systems where there is a 1 and a + but no 2, and hence in such systems "1 + 1 = 2" is not true (but only because it has no meaning; there is no use for a symbol '2' and hence there is none). But any algebraic system with a 1, a +, and a 2 will have 1 + 1 = 2. [Unless someone purposefully makes a senseless interpretation of the symbols]

 

[AKG]

Yeah, it obviously does. But WHAT if it didn't?

Are you calling Hilbert an "it"? :) No listen, the guy said "we defined 1 + 1 to be 2" so we did it, not an "it". So what if we didn't define it that way? Then everything would be the same as it is today, we'd just be using different symbols.

 

[theperthvan]

Not too sure what you're saying.
If you mean that we, mathematicians, human beings, whatever, decided that we will make 1+1=2, then good. Have a lolly.
Even if it is defined differently, the fact still remains that if Bob has an apple and Sally gives him another apple, Bob now has two (whatever two means) apples, which is what I meant. Not really talking about how it is written or what base is being used or any definition stuff, just the concept.

 

[davidpetertuc]

If this were one of the physics forums, I'd probably cite Maxwell's Equations. But since this is the world of math, I'm definitely going to have to go with the Fundamental Theorem of Calculs. But Uart's example was also interesting...



This, I must admit, is pretty awesome. I wonder how it's derived, especially since there's no obvious formula for calculating the nth prime.

This formula is even better. If n=2 then is equals PI^2/6

 

[Mike_Bson]

lim Re(zeta(1 + ix)) = gamma
x to 0

It's awesome because it involves the coolest function ever, and the coolest constant ever.

I tried to write it with Latex, how do I make it appear in my post?

 

[zgozvrm]

I would have to say "I = 1,000,000,000"

where I represents me, and 1,000,000,000 represents the amount of money in my bank account.

 

[n1person]

\int_\Omega \mathrm {d}\omega = \oint_{\partial \Omega} \omega

Stokes Theorem, so useful all the time...

 

[hgfalling]

The story about L'Hopital's rule being work for hire done by Bernoulli because L'Hopital wanted to have something named after him, which now all first year calculus students hear about, is awesome.

 

[OmCheeto]

y=x-sin(x)

(solve for x)

because after 20 years of scratching my head, some smarty said he was going to re-invent math to solve the problem.

I warned him...



(I finally found a "mathematician" that could explain the silliness to me)

 

[Char. Limit]

y=x-sin(x)

(solve for x)

because after 20 years of scratching my head, some smarty said he was going to re-invent math to solve the problem.

I warned him...



(I finally found a "mathematician" that could explain the silliness to me)

But that's easy to solve. x=Om(y), where Om(y) is defined as the inverse of x-sin(x)

 

[OmCheeto]

But that's easy to solve. x=Om(y), where Om(y) is defined as the inverse of x-sin(x)

Gulp. Did you know for the last 15 years I've been offering a $100 to anyone who could either solve the equation, or explain why it could not be solved.

I've never mentioned that at this forum as:
a. There are just way too many smart people here
b. It's a sign of a crackpot

I don't know why people can offer a million dollars for such things(Millennium Prize), but I get a bad label for doing such things.

Maybe I should have called it the "OmCheeto Prize"?

 

[Char. Limit]

Well, I believe you know me on Facebook, so you probably have my address. I expect my $100 within two weeks.

 

[dydxforsn]

I think I have two favorites, first, the infamous Fourier Series:

f(x) = A_o + \sum_{n=1}^{\infty} A_n\cos{\frac{n\pi x}{L}} + \sum_{n=1}^{\infty} B_n\sin{\frac{n\pi x}{L}}

which I think is one of the more interesting ideas in all of mathematics, and obviously one of the more applicable mathematical tools we use in everyday life. Joseph Fourier was truly brilliant to think along these lines (every function can be represented as an infinite series of sine and cosine, well, when you do a Fourier Transform anyway..), though I don't exactly know how much exactly he contributed to the theory of Fourier Series, I'm giving him the benefit of the doubt of total creativity :DSecond, I always liked the simple weighted average:

\bar{x} = \sum_{i=1}^{n} P_i x_i

I guess simply because it's extremely useful and just aesthetic to me, it's just always been on of my favorites, from quantum theory (expectation values) to statistical mechanics (with partition functions, Boltzmanm factors, etc.) it just always takes a conceptual center stage.

 

[Mike_Bson]

Ah, here we go:

\lim_{x\to0}\zeta(1 + ix)=\gamma

 

[Char. Limit]

Ah, here we go:

\lim_{x\to0}\zeta(1 + ix)=\gamma

But I get something different...

Actually, after the addition of \frac{i}{x}, I get the E-M constant.

 

[Sniperman724]

Mine is definitely v=v₀+at

 

[TylerH]

Distance along a curve is my favorite.
\int \sqrt{1-({{dy} \over {dx}})^2}dx

 

[Yayness]

I'm not sure what my favorite is, and I would probably keep switching favorite formula anyway.
I kind of like this one: \pi=\lim_{n\rightarrow\infty}2^n\underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2+\cdots+\sqrt 2}}}}}_{n}
I like it because it goes quicker towards pi than what many other formulas do, but also because I managed to prove it 2 days ago, using regular 2ⁿ-gons.