1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What the heck is this paragraph saying?

  1. Aug 11, 2011 #1
    What the heck is this paragraph saying?
     

    Attached Files:

    • sym.jpg
      sym.jpg
      File size:
      11 KB
      Views:
      74
  2. jcsd
  3. Aug 11, 2011 #2

    Mark44

    Staff: Mentor

    Re: symmetry

    In the first example, x + y + z, it's saying that if you swap, say, x and z, you get an different expression that has the same value.

    IOW, x + y + z = z + y + x

    In the second, bc + ca + ab, you can swap, say b for c, to get a new expression with the same value.
    IOW, bc + ca + ab = cb + ba + ca.

    bc = cb due to commutivity of multiplication, and ab = ba for the same reason. There's also some commutivity of addition going on, as ca + ab = ab + ca.
     
  4. Aug 11, 2011 #3
    Re: symmetry

    so its not talking about x, y, and origin symmetry?
     
  5. Aug 12, 2011 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: symmetry

    No, its is not. It is talking about interchanging the letter variables themselves:
    3x+ 3y is "symmetric" in this sense but x+ 2y is not.
     
  6. Aug 12, 2011 #5
    Re: symmetry

    and x+ 2y is not symmetric because the x and y coefficients are not equal?
     
  7. Aug 12, 2011 #6

    Dembadon

    User Avatar
    Gold Member

    Re: symmetry

    The type of symmetry being discussed here reminds me of binomial expansions.

    [itex](x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}[/itex]

    Notice that the coefficients aren't the only cause of symmetry!
     
  8. Aug 12, 2011 #7
    Re: symmetry

    what do they mean by "symmetry?" what will knowing symmetry of an expression help me with?
     
  9. Aug 12, 2011 #8

    Dembadon

    User Avatar
    Gold Member

    Re: symmetry

    If you can perform some type of transformation to an expression or equation (without murdering it!), then there is a relational symmetry. In other words, the output of a function does not vary when the arrangement of any or all of the variables within the function are changed.

    I'm an amateur, though, so I'm sure HoI or Mark can put it more succinctly or correct anything I've said that is ambiguous, imprecise, or simply incorrect. :redface:

    You will encounter situations where things can be assumed or proven because of symmetrical relationships, and it will often save you a lot of work!
     
  10. Aug 17, 2011 #9

    Dembadon

    User Avatar
    Gold Member

    Re: symmetry

    This video might be helpful to you:
    https://www.youtube.com/watch?v=ylAXYqgbp4M
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What the heck is this paragraph saying?
  1. What the heck? (Replies: 3)

Loading...