Favorite Equation: Quadratic Formula - Solving for X

[murshid_islam]

Ahh but both sides are TRUE, shown by sign to be not equal :) Its still an equation.

no it isn't. how can it be an "equation" if two sides of it are NOT equal?

O and not to mention, they can be equal, he didn't say that a, b and c had to be positive integers.

yeah, they can be equal. but then he would be wrong because he wrote it to be NOT equal.

 

[Gib Z]

aww fine be that way :P Its his favorite INEQUALITY :P

2nd bit, ill be a turd and say maybe he had cartain values of a,b and c in mind and forgot to tell us :P

 

[Alkatran]

isn't this thread about favourite "equations"? but what rock4christ mentioned is not technically an "equation". the two sides are not equal for $$n \geq 3$$. is that a Ramanujan summation? or am i confusing it with something else?

I typed "Ramanujan summation" into my address bar, forgetting to prefix it with "google" and a PDF download immediately started. Apparently Firefox uses I'm feeling lucky, scary.

I've always liked the infinite series equalities learned in first year calculus (power series, e^x, sin/cos, etc). Those blew my mind a lot more than Euler's identity (mainly because they implied it)

 

[Gib Z]

Yes those amazed me a lot as well. Its interesting to observe the properties on the series, and see how they match the original function. I have countless hours of fun finding the derivative of the sine series to get cosines and using the series for e^x to derive eulers formula :P. Eulers formula is cool because its simple, and its not implyed but true :)

 

[murshid_islam]

another fun thing i did with the maclaurin series is finding out different series to calculate the value of pi, e.g., the series for arctan(x).

 

[Gib Z]

Ahh yes that was fun, but usually converge slowly >.< The simplest case, and also the slowest converging is $$\frac{\pi}{4} = \sum_{n=0}^{\infty} \frac{-1^n}{2n+1}$$. I read somewhere it takes 10000 terms just to converge to 3 decimal places >.<

 

[complexPHILOSOPHY]

$$z_{0}=C$$;

$$z_{n+1}=z^2_n+C$$

Not that I pretend to understand it but I certainly appreciate the elegance involved in the mathematics and the visuals it produces are trippy.

 

[tehno]

You like fractals complexPHILOSOPHY,don't you?
I like your choice.

 

[disregardthat]

(cosx)^2+(sinx)^2 = 1

 

[complexPHILOSOPHY]

You like fractals complexPHILOSOPHY,don't you?
I like your choice.

I think all psychedelic heads do, my friend! I was enthralled by the visuals it produced before I even had an interest in mathematics so after discovering the maths behind it, it quickly became something that I truly appreciated.

 

[murshid_islam]

Ahh yes that was fun, but usually converge slowly >.< The simplest case, and also the slowest converging is $$\frac{\pi}{4} = \sum_{n=0}^{\infty} \frac{-1^n}{2n+1}$$. I read somewhere it takes 10000 terms just to converge to 3 decimal places >.<

yeah its the slowest i think. and as far as i remember, the fastest series for $$\pi$$ is the series given by ramanujan.

 

[Gib Z]

Just to re iterate my love for Eulers Formula to Jarle-

$$e^{ix}=\cos x + i \sin x$$
$$e^{-ix}=\cos x - i\sin x$$
Multiplying these two together:
$$\sin^2 x + \cos^2 x=1$$

Euler's formula can lead to that great Pythagorean Identity :D

 

[Gib Z]

Response to murshid_islams comment, there are actually faster series now, but they are all based on the work by ramanujan anyway :)

 

[ssd]

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

 

[radou]

Blah, all of this is too fancy. I'll take 0 + 1 = 1.

 

[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.