Notices
Results 1 to 10 of 10

Thread: distance conjecture

  1. #1 distance conjecture 
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    Alright, I have a conjecture that;

    The shortest distance from some point to the surface of a sphere is the distance from the point to the center of the sphere minus the radius.

    I have a feeling it's already been proven true, but I was just curious what other peoples thoughts on this are.


    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Masters Degree organic god's Avatar
    Join Date
    Feb 2008
    Location
    London
    Posts
    567
    if you look at your statement again you will see that problem is basically.

    "show that the shortest distance between 2 points is a straight line"


    everything is mathematical.
    Reply With Quote  
     

  4. #3 Re: distance conjecture 
    Forum Ph.D. Leszek Luchowski's Avatar
    Join Date
    Jun 2008
    Location
    Gliwice, Poland
    Posts
    807
    Quote Originally Posted by Arcane_Mathamatition
    Alright, I have a conjecture that;

    The shortest distance from some point to the surface of a sphere is the distance from the point to the center of the sphere minus the radius.
    This is only true for points outside or on the surface of the sphere.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
    Reply With Quote  
     

  5. #4  
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    no, it's true for ALL points in . I'm not quite sure how to prove it, but I'd love a counter example if you could provide one.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  6. #5  
    Forum Ph.D. Leszek Luchowski's Avatar
    Join Date
    Jun 2008
    Location
    Gliwice, Poland
    Posts
    807
    Quote Originally Posted by Arcane_Mathamatition
    no, it's true for ALL points in . I'm not quite sure how to prove it, but I'd love a counter example if you could provide one.
    Sphere centered at (0,0,0), radius 1.

    Point (0,0,.5).

    Distance to surface: .5

    Distance to center: .5

    Distance to center minus rarius: -.5

    -.5 is not equal .5

    How was that for a counterexample?
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
    Reply With Quote  
     

  7. #6  
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    shouldn't distance always be positive? Wouldn't you need an absolute value there? Or, conversely, since the point is WITHIN the sphere, I could say it's distance is negative, as you would assume the distance to be towards the center of the sphere as opposed to away from it. so you would need to move a distance of .5 negative to the center.
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  8. #7  
    Forum Ph.D. Leszek Luchowski's Avatar
    Join Date
    Jun 2008
    Location
    Gliwice, Poland
    Posts
    807
    Quote Originally Posted by Arcane_Mathamatition
    shouldn't distance always be positive? Wouldn't you need an absolute value there?
    This is precisely what was wrong about your conjecture. A distance should always be non-negative (positive or zero). For points inside the sphere, the difference in your conjecture is not. Put in an absolute value and your conjecture will be right.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
    Reply With Quote  
     

  9. #8  
    Forum Isotope
    Join Date
    Feb 2009
    Location
    Transient
    Posts
    2,914
    but isn't a distance DEFINED as an absolute value? so by claiming I want a distance, don't I already imply absolute value?
    Wise men speak because they have something to say; Fools, because they have to say something.
    -Plato

    Reply With Quote  
     

  10. #9  
    Forum Ph.D. Leszek Luchowski's Avatar
    Join Date
    Jun 2008
    Location
    Gliwice, Poland
    Posts
    807
    Quote Originally Posted by Arcane_Mathamatition
    but isn't a distance DEFINED as an absolute value? so by claiming I want a distance, don't I already imply absolute value?
    You gave a recipe which was in fact a formula except it was written with words rather than symbols: "this" minus "that", period. This left no room for taking into account what you may have implied elsewhere. Mathematics is an exact science.

    Besides, there are other ways of turning a possibly negative value into a guaranteed nonnegative one: taking its square or any other even power, or exp(x) (i.e. inverse natural logarithm), and lots more. Unless you specify which of those you want, your hints at "wanting a distance" (and therefore implicitly a nonnegative value) don't make a completely defined algorithm.
    Leszek. Pronounced [LEH-sheck]. The wondering Slav.
    History teaches us that we don't learn from history.
    Reply With Quote  
     

  11. #10 Re: distance conjecture 
    . DrRocket's Avatar
    Join Date
    Aug 2008
    Posts
    5,486
    Quote Originally Posted by Arcane_Mathamatition
    Alright, I have a conjecture that;

    The shortest distance from some point to the surface of a sphere is the distance from the point to the center of the sphere minus the radius.

    I have a feeling it's already been proven true, but I was just curious what other peoples thoughts on this are.
    Your conjecture is equivalent to the shortest distance to the sphere is along a line that is normal to the sphere. This is true.
    Reply With Quote  
     

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
  •