Stories
Slash Boxes
Comments

News for nerds, stuff that matters

Slashdot Log In

Log In

Create Account  |  Retrieve Password

Greatest Equations Ever

Posted by timothy on Mon Oct 25, 2004 04:21 AM
from the comic-shop-guy's-revenge dept.
sgant writes "What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New York Times article about the same poll. Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, ei + 1 = 0. What are some of your favorite equations?"
+ -
story
This discussion has been archived. No new comments can be posted.
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
 Full
 Abbreviated
 Hidden
More
Loading... please wait.
  • correction (Score:5, Insightful)

    by schematix (533634) * on Monday October 25 2004, @04:23AM (#10618970) Homepage
    Euler's equation is actually Exp[i*Pi] + 1 = 0 not Exp[i*n] +1 = 0 (unless they say n = Pi, which they don't). I'd have to say this is the most elegant equation of all time. It combines the 5 most important numbers in all of mathematics into a single formula. This formula also has tremendous applications in many fields of engineering and other areas of applied mathematics. If it wasn't for this equation, your cell phone wouldn't work.
    • Re:correction (Score:5, Insightful)

      by niks42 (768188) on Monday October 25 2004, @04:36AM (#10619025)
      Actually, isn't Euler's formula Exp[i*theta] = cos[theta] + i*sin[theta] ? and then substitute in the value of pi into theta, and the more famous result appears.
      • Re:correction (Score:5, Informative)

        by Anonymous Coward on Monday October 25 2004, @04:53AM (#10619085)
        There's a difference between "Euler's formula" and "Euler's Formula", depending on whether you're referring to one of his formulae or the specific formula called "Euler's Formula".

        Guy created so many darn formulae that "Euler's formula" is ambiguous.
      • Re:correction (Score:5, Interesting)

        by SamSim (630795) on Monday October 25 2004, @05:09AM (#10619148) Homepage Journal

        ...Which is in turn not to be confused with Euler's equation, which is V+F=E+2.

        Euler has a ridiculous amount of stuff named after him.

    • Re:correction (Score:5, Informative)

      by Ford Prefect (8777) on Monday October 25 2004, @04:43AM (#10619058) Homepage
      It combines the 5 most important numbers in all of mathematics into a single formula.

      It's also got the other important mathematical concepts - exponentiation (i.e. raising something to the power of something else), multiplication, addition and equals. Essentially, it's a huge nugget of maths in a tidy little wrapper.

      I've got an old Sharp graphics calculator, which has both proper notation layout and a complex numbers mode. I still like keying in the 'e^(pi*i)+1', pressing 'Enter', then getting the zero, all perfectly laid out on a little LCD display...
      • by Anonymous Coward on Monday October 25 2004, @04:54AM (#10619089)
        Too bad my mathematical abilities don't reach beyond spelling rude words on calculators held upside-down.

        Oh well. 5318008.
        • Joke Time (Score:5, Funny)

          by TrentL (761772) on Monday October 25 2004, @07:27AM (#10619653) Homepage
          George Bush still doesn't know if Bin Laden is alive! After numerous rounds of "We don't even know if Osama is still alive", Osama himself decided to send George Bush a message in his own handwriting to let him know that he was still in the game.
          Bush opened the letter and it appeared to contain a coded message:

          370HSSV-0773H

          Bush was baffled, so he typed it out and e-mailed it to Colin Powell. Colin and his aides had no clue either so they sent it to the CIA. No one could solve it, so it went to the NSA and then to MIT and NASA and the Secret Service.

          Eventually they asked Britain's M I6 for help. They cabled the White House: "Tell the President he is looking at the message upside down."
        • by UnknowingFool (672806) on Monday October 25 2004, @08:48AM (#10620119)
          Too bad my mathematical abilities don't reach beyond spelling rude words on calculators held upside-down.

          Oh well. 5318008.

          Wouldn't it more appropriate to be: 55378008

    • Actually... (Score:4, Insightful)

      by yoshi_mon (172895) on Monday October 25 2004, @04:46AM (#10619066)
      If it wasn't for this equation, your cell phone wouldn't work.

      If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
      • Re:Actually... (Score:5, Insightful)

        by Rich0 (548339) on Monday October 25 2004, @06:34AM (#10619454) Homepage
        e^i*pi=-1 isn't a law of nature.

        It is a mathematical relationship which is completely abstract - none of those values are physical quantities, although all of them are used in other physical equations.

        In theory an alien in a completely different universe could come up with the same formula.

        Think about it - e is related to the integral of 1/x on a flat plane - which doesn't exist in real life. i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience). Pi is a number which is very useful in practical measurements, but which can be described completely in the abstract.

        In any case, an equation like Euler's formula reflects our understanding of mathematics in general more than it reflects our knowledge of any particular physical process.
        • Re:Actually... (Score:5, Interesting)

          by rsidd (6328) on Monday October 25 2004, @08:53AM (#10620156)
          i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience).

          Quantum mechanical wavefunctions are complex. You could define them as two real wavefunctions and work out the appropriate algebra, but it's exactly complex algebra. So i could correspond to the phase difference of two wavefunctions, which would be observable via interference effects.

          Not disagreeing with what you're saying though -- the equation is fundamental mathematics, independent of the physical universe, it doesn't make sense to imagine an "alternative universe" where it doesn't apply.

      • by dwbassett42 (752317) on Monday October 25 2004, @06:43AM (#10619485) Homepage
        This difference in views is similar to a fundamental difference between engineers and physicists: Engineers feel their equations are a reasonable approximation of reality, and physicists feel that reality is a reasonable approximation of their equations. And mathematicians? They see no relation between the two. ;)
      • by Smidge204 (605297) on Monday October 25 2004, @07:28AM (#10619654)
        Nonono, any researcher will tell you that. They just want to cover up the TRUTH. Those complex mathematical formulas are actually mystical runes that describe ancient spells. The formulas themselves DO make your phone work!

        =Smidge=
  • sum of cubes (Score:5, Interesting)

    by themusicgod1 (241799) <themusicgod1@@@zworg...com> on Monday October 25 2004, @04:23AM (#10618971) Homepage Journal
    a^3+b^3 = (a+b)(a^2-ab+b^2)
    first proof, that i'd seen at least, of the existance of negative numbers.
    • by Kippesoep (712796) on Monday October 25 2004, @08:13AM (#10619876) Homepage
      I wish I could deny the existence of negative numbers. My bank, on the other hand, insists that is how much money I have...
      • Re:sum of cubes (Score:5, Interesting)

        by themusicgod1 (241799) <themusicgod1@@@zworg...com> on Monday October 25 2004, @04:58AM (#10619107) Homepage Journal
        I mean, you're right it does. But man, was I skeptical.

        I say, that until I saw the sum of cubes I internally denied the existance of negative numbers. I mean I could work with them and all, I just didn't believe in them. If you deny the existance of negative numbers, you cannot have an expression 0-1, because -1 is meaningless, so therefor the result is meaningless. It's circular reasoning, and this is why[according to my youthful very non-standard way of thinking of things]:

        there is a number -1
        there is a number 0
        if you have two numbers, there is a third number which represents their sum. :.
        there is a number -1 + 0

        if there is a number -1 + 0 there must be a class of numbers known as negative numbers
        [the direction you were going in?]
        but if you cannot prove there is a number -1 + 0, you cannot even get that far.

        a^3+b^3 = (a+b)(a^2 - ab + b^2 ), on the other hand, shows quite clearly that no matter what numbers a and b you pick, you end up, in your equation, with a negative number.
  • V=IR (Score:5, Interesting)

    by oddbudman (599695) on Monday October 25 2004, @04:23AM (#10618973) Journal
    Gotta Love V=IR. Works pretty well, I use it daily, well that and P=VI.
    • Re:V=IR (Score:5, Interesting)

      by djdead (135363) <sethNO@SPAMwenchel.com> on Monday October 25 2004, @06:12AM (#10619382)
      When I was taking physics for the first time in high school, a EE from MIT taught me the following:

      twinkle twinkle little star
      power equals I squared R

      I remembered it.
      • Re:V=IR (Score:5, Funny)

        by Quantum Jim (610382) <jfcst24&yahoo,com> on Monday October 25 2004, @11:33AM (#10621744) Homepage Journal

        There was once a football player who was teetering on the edge of academic eligibility. To help the poor guy with his physics test, the coach told him:

        Remember this ryme, to get the power in a circuit:
        Twinkle twinkle little star,
        Power equals I squared R.

        Well the school day before the exam, the football player also had a big game. He tackled alot of people and had a really good day. However, the next day he failed his test! The coach couldn't understand, so he asked the player if he remembered the ryme. The football player said:

        Of course, coach:
        Twinkle twinkle star in the sky,
        Power equals R squared I!

        There's a moral in there somewhere. :-)

  • by oneandoneis2 (777721) * on Monday October 25 2004, @04:23AM (#10618975) Homepage
    Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, e^in + 1 = 0. What are some of your favorite equations?"

    Take a look at the username, and take a guess at mine :o)

  • Geometry and Algebra (Score:5, Interesting)

    by metlin (258108) * <narayan@f a s . h a r v ard.edu> on Monday October 25 2004, @04:24AM (#10618979) Homepage Journal
    In my opinion, the most important equations are those that brought together Algebric representation of Geometry -- that has been the single most fundamental basis for today's advancement in mathematics and physics.
  • Well... (Score:5, Funny)

    by Anonymous Coward on Monday October 25 2004, @04:24AM (#10618981)
    I'm quite fond of this one...

    B*u*pi * integral of e^x

    Hint: Try writing it in mathematical notation.

  • H = F ^ 3 (Score:4, Insightful)

    by Rob_Warwick (789939) <warwick@@@applefritter...com> on Monday October 25 2004, @04:28AM (#10618996) Homepage Journal
    Happiness = Food x Friends x Fun
    From Woz.

    It's the most important and beautiful equation I've ever seen.
  • by bokmann (323771) on Monday October 25 2004, @04:30AM (#10619010) Homepage
    My favorite is the thinkgeek tshirt that says "2+2=5 for extremely large values of 2".

    It is not just funny... if you consider the numbers not as integers, but as any float value with that integer as the first number, it is true.
  • by Jesrad (716567) on Monday October 25 2004, @04:31AM (#10619012) Journal
    ih/2Pi dPhi/dt = hc/2iPi (A1 dPhi/dx1 + A2 dPhi/dx2 + A3 dPhi/dx3) + A4 mc(squared)Phi

    Said by Hotson to be the Equation of Everything. First part [zeitlin.net], second part [zeitlin.net]. Worth a read IMO.
  • 0 = 0 (Score:5, Funny)

    by RAMMS+EIN (578166) on Monday October 25 2004, @04:33AM (#10619018) Homepage Journal
    My favorite is 0 = 0, because it's the one that most often indicates you're done with the math exercise. :-)
  • dupe of old poll (Score:5, Informative)

    by Gathers (78832) on Monday October 25 2004, @04:38AM (#10619031) Homepage
    "What is your favorite equation? ..."
    Shashdot has already covered this in a poll! We all already know that E=mc^2 is the overall favorite, closely followed by F=ma.
    http://slashdot.org/pollBooth.pl?qid=804 [slashdot.org]
  • by physicsphairy (720718) on Monday October 25 2004, @04:39AM (#10619043) Homepage
    The equation everyone knows offhand is E=mc^2 (even if they don't know what it means), but few people know that the full equations is E=m^2c^4 + p^2c^2. 'p' is momentum, so when you're talking about just the rest mass of the particle you have E=mc^2.

    Anyway, just thought I'd share that because E=m^2c^4 + p^2c^2 is my favorite equation and most people think it looks a little familiar but wouldn't know what it was without a little additional explanation.

  • by Ibag (101144) on Monday October 25 2004, @04:41AM (#10619049)
    The integral of a differential form on the boundry of a manifold is equal to the integral of the exterior derivative on the manifold itself.

    S_{dM)w=S_(M)dw

    An important special case is the fundamental theorem of calculus. Not only is this a beautiful looking theorem, but important too.

    Other special cases are the classical forms of green's theorem, stoke's theorem, and the divergence theorem.

    I dunno if its my favorite equation, but its up there.
  • by marcovje (205102) on Monday October 25 2004, @04:43AM (#10619057)

    Everything = 42 :-)
  • by lewger (648379) on Monday October 25 2004, @04:51AM (#10619078) Journal
    I always liked this one that my calc teacher says he saw once on a students paper
    Sin x / n = 6
    The logic of this was that the n on the bottom cancelled out the n on the top so the result was Six. Oh well I laughed when I was shown it.
  • 1+1=10 (Score:5, Funny)

    by notany (528696) <notany.gmail@com> on Monday October 25 2004, @05:13AM (#10619161) Journal

    There are 10 kinds of people: those who understand binary and those who don't.
  • by jolyonr (560227) on Monday October 25 2004, @05:36AM (#10619254) Homepage
    Of special importance to slashdot:

    garbage in = garbage out
    Jolyon
  • by tootlemonde (579170) on Monday October 25 2004, @05:58AM (#10619332)
    Over at the Historia-Matematica [mathforum.org] discussion list, the members debated [mathforum.org] a similar question:

    As you know, notation has helped the progress of mathematics. Consider, for example, the limitations of the Roman number system, the importance of the invention of a symbol for zero, etc.

    Which were, in your opinion, the notations that have permitted the greatest advances in mathematics?

    Apropos to the current discussion was this response [mathforum.org]:

    the interest of the question:

    > Which were, in your opinion, the notations that have permitted the
    > greatest advances in mathematics?

    (which is very different from any question concerning the history of math. notations) is very close to the interest of the question: who has been the greatest mathematician in the history, e.g. near zero.

  • by tod_miller (792541) on Monday October 25 2004, @06:29AM (#10619430) Journal
    us {all,your,base}

    Of course if sets aren't your thing...
  • by dysprosia (661648) on Monday October 25 2004, @06:29AM (#10619431)
    I would have to say, at the moment, my favorite equation would have to be the one giving the coefficients of the generalized Fourier series [wikipedia.org] involving a set of eigenfunctions {p_n}, ie., c_n = <f, p_n>/||p_n||^2.

    Simple stuff, but incredibly cool, considering that Fourier series don't always have to involve just sines and cosines, and you get similar sorts of behaviour.
  • by ortholattice (175065) on Monday October 25 2004, @06:35AM (#10619457)
    The answer is simple. The most beautiful equations, hands down, are those from which all of mathematics can be derived. These are the axioms of ZFC set theory. What could possibly be more beautiful or more important than that? And it's a shame so few people know about them. See Zermelo-Fraenkel Axioms [wolfram.com] and Metamath Proof Explorer [metamath.org].
  • Another.. (Score:5, Interesting)

    by deego (587575) on Monday October 25 2004, @06:44AM (#10619489) Homepage

    Z = z^2 + c

    ^^ This simple equation is the generator of Mandelbrot (and Julia) set, arguably the richest fractal known to us..