Notices
Results 1 to 35 of 35
Like Tree3Likes
  • 2 Post By Strange
  • 1 Post By mvb

Thread: Terminology

  1. #1 Terminology 
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Can anyone tell me if equations of the form illustrated by the following example;



    have a name?

    In general, I would be inclined to represent them as;



    but I am not sure that this would be seen as the most appropriate general expression.


    Reply With Quote  
     

  2.  
     

  3. #2  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    ax^2+by^2+cx+dy+e=0
    used for circles called the general eqn of a circle
    i got x=y^2/y-1


    Last edited by fiveworlds; February 7th, 2013 at 09:44 AM.
    Reply With Quote  
     

  4. #3  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Quote Originally Posted by fiveworlds View Post
    ax^2+by^2+cx+dy+e=0
    used for circles called the general eqn of a circle
    i got x=y^2/y-1
    Thank you for taking the time to comment, but my question does not refer to any particular function of x and y - the expression I gave was merely an example chosen at random.

    I have two questions:

    1) is there a name for equations of the type ?

    Any such equation will obviously be solved by pairs of values where provided that the function exists for the values chosen.

    2) is the appropriate way of denoting the function? My reason for wondering about this is that, usually, the expression does not specify the order in which x and y are written, but in the equation I gave above, the order if clearly important. For example, is there some other way of writing it such as indicating that the value of the function not only depends on the values of x and y but that the order is important? This is a detail that I am not much concerned about. The main question is Q1.
    Reply With Quote  
     

  5. #4  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    unfortunately not jonG the equations f(x,y)=f(y,x) assignment statements probably or just functions they could be anything one function using this can solve riemann one solve for a circle. you have no idea of how something changes between the two points it could be a curve or an alternating waveform or a square wave etc. Anything can be that eqn literally anything .i gave your above equation an attempt im afraid im abit rusty on my maths so ill post it later when i have time.Any eqn of known distance can be rotated through 360 degrees. In any equation x always equals y or r always equals i and one is always 1/2 of the other
    Last edited by fiveworlds; February 7th, 2013 at 10:57 AM.
    Reply With Quote  
     

  6. #5  
    mvb
    mvb is offline
    Thinker Emeritus
    Join Date
    Dec 2012
    Location
    Delaware, USA
    Posts
    195
    In physics, an equation where f(x,y) = f(y,x) would be called a symmetric equation, or to be explicit an equation that is symmetric in its arguments. I'm not sure whether this description would be used in mathematics.
    Reply With Quote  
     

  7. #6  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    I have wondered about the term symmetric, but it seems to cover too many options - symmetry about the x-axis and/or symmetry about the y-axis.
    The solutions to are symmetric about the line y = x but not about the x or y axes. If is a solution then so is .

    My reason for wanting to find a name is simply in an attempt to find out more about equations of this type.
    Reply With Quote  
     

  8. #7  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    According to Wikipedia:
    A symmetric function of n variables is one whose value at any n-tuple of arguments is the same as its value at any permutation of that n-tuple. While this notion can apply to any type of function whose n arguments live in the same set, it is most often used for polynomial functions, in which case these are the functions given by symmetric polynomials. There is very little systematic theory of symmetric non-polynomial functions of n variables, so this sense is little-used, except as a general definition.
    Symmetric function - Wikipedia, the free encyclopedia

    So you may be breaking new ground
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  9. #8  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    the thing is i dont know a single non symmetrical eqn. do you?
    Reply With Quote  
     

  10. #9  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by fiveworlds View Post
    the thing is i dont know a single non symmetrical eqn. do you?
    To pinch the example from Wikipedia:
    Consider now the function


    If x and y are interchanged, the function becomes

    This function is obviously not the same as the original if , which makes it non-symmetric.
    Although, the OP seems to be trying to do something slightly different and make these two equal...
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  11. #10  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    graph anything and you always have two points through a distance these points can turn through 360 degrees easy in a different section of this circle f(x,y)=x^2+y would be the exact same as f(y,x)=x+y^2
    Reply With Quote  
     

  12. #11  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Some punctuation to indicate your sentences might make what you are trying to say a little clearer.

    But making a guess at it...

    Quote Originally Posted by fiveworlds View Post
    graph anything nd you always have two points through a distance these points can turn through 360 degrees
    I don't believe the graph of every function is rotationally symmetrical. In fact I know it isn't. (And it has nothing to do with the OP)
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  13. #12  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    and if you have a line anything with the x and y axis is there always an x and y coord??
    Reply With Quote  
     

  14. #13  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by fiveworlds View Post
    and if you have a line anything with the x and y axis is there always an x and y coord??
    Sorry, I don't know what that means. Do you want to try again with full English sentences.
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  15. #14  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    well if you have an x and a y co-ord then changes in x must be proportional to changes in y and therefore there is a symmetry between x and y . Since axis are generally used in maths then your maths must have a symmetry to your axis.
    Reply With Quote  
     

  16. #15  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by fiveworlds View Post
    well if you have an x and a y co-ord then changes in x must be proportional to changes in y and therefore there is a symmetry between x and y .
    Here is a simple equation that produces a graph which is not symmetrical:

    Graph here: http://www.wolframalpha.com/input/?i=2^%281%2Fx^3%29
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  17. #16  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    there is a symmetry there x is getting smaller to infinity
    Reply With Quote  
     

  18. #17  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Do you know what the word "symmetry" means?
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  19. #18  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    yeah a relationship/proportion. and you have the proportions ie function
    Reply With Quote  
     

  20. #19  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by fiveworlds View Post
    yeah a relationship/proportion.
    Er, no. Maybe that is why we have been talking at cross purposes.

    In it's simplest, symmetry defines operations that you can do to something to leave it unchanged. For example a square is symmetric because you can rotate it through 90 degrees. A rectangle is symmetric because you can flip it horizontally or vertically and it will look the same. But a glove is not symmetric there is no series of rotations or transformations that will give you the same shape.
    fig8a.jpg

    Beyond that, it gets deeply mathematical.
    JonG and mvb like this.
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  21. #20  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    flip 90 degrees 180degrees 24.674367238 degrees same shape. turn your hand to the left does it still look like a hand???
    Reply With Quote  
     

  22. #21  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by fiveworlds View Post
    flip 90 degrees 180degrees 24.674367238 degrees same shape
    What is? And, no, not if it not symmetrical.

    To go back the the glove example. There is no way to change a left hand glove to a right hand glove: any set of rotations and transformations will not do it. Because it does not have symmetry.
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  23. #22  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    so if you take your shoe and turn it to your left is it not a shoe?ps a left hand glove and right hand glove are different functions you cant make radius = plane
    Reply With Quote  
     

  24. #23  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Quote Originally Posted by Strange View Post
    According to Wikipedia:
    A symmetric function of n variables is one whose value at any n-tuple of arguments is the same as its value at any permutation of that n-tuple. While this notion can apply to any type of function whose n arguments live in the same set, it is most often used for polynomial functions, in which case these are the functions given by symmetric polynomials. There is very little systematic theory of symmetric non-polynomial functions of n variables, so this sense is little-used, except as a general definition.
    Symmetric function - Wikipedia, the free encyclopedia




    So you may be breaking new ground
    Thank you Strange - the link is the sort of thing I am looking for, but I didn't expect "symmetric function" to find it. As for breaking new ground - I have done it often - it's called gardening.
    Reply With Quote  
     

  25. #24  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    oh i love gardening we may exchanges ideas sometime gardenening lots of fun and you get veg out of it and study biology and cook (chemistry). im sure strange would like it.
    Reply With Quote  
     

  26. #25  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Quote Originally Posted by Strange View Post
    To pinch the example from Wikipedia:
    Consider now the function


    If x and y are interchanged, the function becomes

    This function is obviously not the same as the original if , which makes it non-symmetric.
    Although, the OP seems to be trying to do something slightly different and make these two equal...

    Yes - that is right. The symmetry I have referred to is symmetry related to the solutions of , not the symmetry of the function itself.
    Last edited by JonG; February 7th, 2013 at 02:04 PM. Reason: punctuation
    Reply With Quote  
     

  27. #26  
    mvb
    mvb is offline
    Thinker Emeritus
    Join Date
    Dec 2012
    Location
    Delaware, USA
    Posts
    195
    Quote Originally Posted by JonG View Post

    Yes - that is right. The symmetry I have referred is symmetry related to the solutions of not the symmetry of the function itself.
    Oh. As a physicist I am more familiar with the solutions of f(x,y) given that f(x,y) = f(y,x). My immediate reaction to your problem is thus to write

    F(x,y) = f(x,y) - f(y,x)

    in which case the solutions you are talking about are identically the solutions of F(x,y) = 0, since that is your equation rewritten. Now notice that

    F(y,x) = - F(x,y)

    i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

    As a side note, if f(x,y) is symmetric under interchange of x and y, the equation for F becomes

    F(y,x)=0 identically

    and you have no information at all.
    JonG likes this.
    Reply With Quote  
     

  28. #27  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    if the function itself is symmetrical does this not imply that the solutions are too i would imagine so you view something as anti symmetric but how if you take blocks out of a container in a certain order you can also replace them in the same or an alternate order.
    Reply With Quote  
     

  29. #28  
    mvb
    mvb is offline
    Thinker Emeritus
    Join Date
    Dec 2012
    Location
    Delaware, USA
    Posts
    195
    Yes, if f(x,y) is symmetrical under interchange of x and y, all solutions of f(x,y) = 0 are also, and similarly if f(x,y) is antisymmetrical.
    Reply With Quote  
     

  30. #29  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Quote Originally Posted by mvb View Post

    i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

    Yes, that is right. The solutions can be antisymmetric. If (x,y) = (a,b) is a solution, then so is (x,y) = (-a,-b). However, as you also indicate, one needs to be more specific about f(x,y) - for example, is it well-defined for negative values of x or y?
    Reply With Quote  
     

  31. #30  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    mvb if you take the blocks in your container and upturn it making a jenga stack then magnetise each of the blocks so its suspended in midair can you now remove any block keeping shape?
    Reply With Quote  
     

  32. #31  
    mvb
    mvb is offline
    Thinker Emeritus
    Join Date
    Dec 2012
    Location
    Delaware, USA
    Posts
    195
    Quote Originally Posted by JonG View Post
    Quote Originally Posted by mvb View Post

    i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

    Yes, that is right. The solutions can be antisymmetric. If (x,y) = (a,b) is a solution, then so is (x,y) = (-a,-b). However, as you also indicate, one needs to be more specific about f(x,y) - for example, is it well-defined for negative values of x or y?
    That wasn't what I meant by antisymmetric, sorry I missed the ambiguity. What I was talking about was f(x,y) = - f(y,x)
    Reply With Quote  
     

  33. #32  
    mvb
    mvb is offline
    Thinker Emeritus
    Join Date
    Dec 2012
    Location
    Delaware, USA
    Posts
    195
    Quote Originally Posted by fiveworlds View Post
    mvb if you take the blocks in your container and upturn it making a jenga stack then magnetise each of the blocks so its suspended in midair can you now remove any block keeping shape?
    Sorry, I don't understand this at all. In any event, I don't know of any useful analogies between blocks in a container and solutions of a function.
    Reply With Quote  
     

  34. #33  
    Suspended
    Join Date
    Apr 2012
    Posts
    690
    thats okay i know all about jenga. though i know sometimes its good to keep a container
    Reply With Quote  
     

  35. #34  
    Brassica oleracea Strange's Avatar
    Join Date
    Oct 2011
    Location
    喫茶店
    Posts
    17,036
    Quote Originally Posted by mvb View Post
    Sorry, I don't understand this at all. In any event, I don't know of any useful analogies between blocks in a container and solutions of a function.
    Not even knapsack functions ?
    ei incumbit probatio qui dicit, non qui negat
    Reply With Quote  
     

  36. #35  
    Forum Junior
    Join Date
    Sep 2011
    Location
    Manchester, UK
    Posts
    236
    Quote Originally Posted by mvb View Post
    That wasn't what I meant by antisymmetric, sorry I missed the ambiguity. What I was talking about was f(x,y) = - f(y,x)
    It can become confusing - I had to look at what I had written more than once - and even then, wasn't sure that it said what I intended.
    Just to be clear as to what I mean by the solutions being antisymmetric: - imagine a graph of for both positive and negative values of x. Half of the graph will be in the upper right quadrant and the other half in the lower left quadrant. If is a point on the part in the upper right quadrant, then will be a point in the lower left quadrant. Changing the sign of x, changes the sign of y. The solutions of can be points on a plot with the same general shape as the graph of . It won't be exactly the same graph, of course, but it can have the same topology.
    Last edited by JonG; February 9th, 2013 at 07:14 AM. Reason: incorrect word
    Reply With Quote  
     

Similar Threads

  1. Prime Factorisation other Terminology
    By talanum1 in forum Mathematics
    Replies: 3
    Last Post: December 22nd, 2011, 07:33 AM
  2. Ice age terminology
    By Pong in forum Earth Sciences
    Replies: 4
    Last Post: August 13th, 2009, 06:16 AM
  3. Terminology
    By thyristor in forum Mathematics
    Replies: 9
    Last Post: April 27th, 2009, 02:05 PM
  4. Another terminology problem
    By Leszek Luchowski in forum Mathematics
    Replies: 5
    Last Post: September 26th, 2008, 10:10 AM
  5. Cancer terminology
    By tridimity in forum Biology
    Replies: 2
    Last Post: September 3rd, 2008, 03:10 AM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •