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Thread: Namiing two points which have the same spatial coordinates.

  1. #1 Namiing two points which have the same spatial coordinates. 
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    Dear members,

    I had written this following question in the thread Introduce Yourself, I realized it, so I present the question here:

    I would like to ask a question quickly, in case some member can answer it.
    The question is:

    How do I write mathematically the following idea or sutuation:

    There is a line from the point A to the point B (a --->b)
    then another line 45 degrees (in relation to the x axes) right from the point B to the point C (b---->c)
    and then 45 degrees left (in relation to the x axes) from the point C to the point D (c --->d)
    Would it be correct to write this as:
    a--->b:b--->c:c--->d for example?
    What I want to know is how to represent mathematically two points which have exactly the same coordinates.

    Thank you by advance.


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  3. #2  
    Your Mama! GiantEvil's Avatar
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    Any coordinate in an n-dimensional space will be expressed as an ordered n-tuple of numbers. Ex... (a,b) for a plane.
    Two distinct points may not have the same coordinates. Any unique set of coordinates corresponds to only one point.


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    Somebody else will probably give you a better answer, but if you have points like C and D and they are both exactly the same point, I would just write C = D. My definition of equality is two things that are interchangeable, with the only exceptions being referring to the symbols themselves (for instance, 2 + 2 and 4 are interchangeable because they are equal, but not in the sense of referring to the symbols. The statement "2 + 2 needs four strokes to write" is true, but "4 needs four strokes to write" is not).
    This is just what I think.
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    A to B to C three lines going up at 45 degree angles. line segment a to b,bto c,c to d fair enough ok.resultant vector would geometricly be point a to point d in a straight line if that is what you were looking for.as for points themselves by their definition, two of them cannot occupy the same spacial coordinates ,only one at a time,without being the same singular point.as for a line segment .an infinate number of points can ocupy a line segment.that is unusuall as that when the ends of the line segments are reached only one point can occupy that coodinate.
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  6. #5  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by Raspberry red View Post
    There is a line from the point A to the point B (a --->b)
    then another line 45 degrees (in relation to the x axes) right from the point B to the point C (b---->c)
    and then 45 degrees left (in relation to the x axes) from the point C to the point D (c --->d)
    Like this?
    Code:
           D
            \
             \
              C
             /
            /
    A ---- B
    Except there are no two points that are the same...

    Or are you just trying to describe an equilateral triangle? No, because that would be 60 degrees...

    What I want to know is how to represent mathematically two points which have exactly the same coordinates.
    Something like this?

    A = (xa,ya)
    B = (xb,yb)

    Where:
    xa = xb and ya = yb
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  7. #6  
    KJW
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    Naming two points which have the same spatial coordinates
    I may be missing the point, but why can't you give them the same name?
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    There are no paradoxes in relativity, just people's misunderstandings of it.
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    took a while but i think i get it now.from a line along an x axis to below the line then back up returning to x.you will have just to specify at least a y coordinate or a y an z coordinate to specify its location along x.
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  9. #8  
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    Hello dear members,

    Thank you for all your answers and observations above.
    To make it more clear:



    There is an object at F1 which is at rest before the Fall,
    the object stops falling at F3 - which is also the beginning of the rest R1,
    the object is at rest from R1 until R3,
    the object climbs at C1 - which is also R3 - until C3

    I would like to know if it is correct to write the "equation" like I did it above.
    I tried to describe better what I meant and I joined the drawing above.

    Thank you for your observations and contributions.
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  10. #9  
    Brassica oleracea Strange's Avatar
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    I don't think your notation really works. In geometric diagrams it is normal to describe lines by their end points:
    For example, A---------------------B would just be called the line AB.

    Or to define them by the (x,y) coordinates of the endpoints. Or the (x.y) coordinate of the origin plus an angle and a length.

    It is not clear from your diagram what B refers to. Also, the three lines (F1F2, R1R2, and C1C2) are not equal because they have different directions. However, their lengths (magnitudes) could be equal.

    The usual notation for length (I think, my math is very rusty!) of a line AB is |AB|.

    So, it looks like you are trying to say:
    B = |F1F2| = |R1R2| = |C1C2|

    In other words, B is the length of the three lines. Is that correct?
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  11. #10  
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    Quote Originally Posted by Strange View Post
    I don't think your notation really works. In geometric diagrams it is normal to describe lines by their end points:
    For example, A---------------------B would just be called the line AB.

    Or to define them by the (x,y) coordinates of the endpoints. Or the (x.y) coordinate of the origin plus an angle and a length.

    It is not clear from your diagram what B refers to. Also, the three lines (F1F2, R1R2, and C1C2) are not equal because they have different directions. However, their lengths (magnitudes) could be equal.

    The usual notation for length (I think, my math is very rusty!) of a line AB is |AB|.

    So, it looks like you are trying to say:
    B = |F1F2| = |R1R2| = |C1C2|

    In other words, B is the length of the three lines. Is that correct?
    Thank you for your reply Strange,

    B is the bounce.
    F3 has got the same coordinates than R1, and R3 has got the same coordinates than C1, in a 3-dimensional space configuration (where the bounce of a ball takes place).
    F, R, anc C are periods of time, respectively for the falling state, the resting state, and the climbing state of the ball.
    F1, F2, F3 are instants of the falling period
    R1, R2, R3 are instants of the resting period (when the ball is not falling, nor climbing)
    C1, C2, C3 are instants of the climbing period.

    Now, we can observe that there is a "limit point" between the last instant of the falling state F3 and the first instant of the resting state R1, same for the last instant of the resting state R3 and the first instant of the climbing state C1.

    My question is about those points F3-R1, R3-C1, they have the same coordinates, so how can we write them?
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  12. #11  
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    Quote Originally Posted by Raspberry red View Post
    My question is about those points F3-R1, R3-C1, they have the same coordinates, so how can we write them?
    I would refer you to post 6

    Why not call F1 "A", call F3/R1 "B", call R3/C1 "C" and call C3 "D". As you are dealing with straight lines, there doesn't seem to be any need to label the middle of the lines.

    Then you have: the ball falls from A to B, it rests from B to C, and it climbs from C to D. You can refer to the periods of time as tAB tBC and tCD.
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  13. #12  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Raspberry red View Post
    My question is about those points F3-R1, R3-C1, they have the same coordinates, so how can we write them?
    I would refer you to post 6

    Why not call F1 "A", call F3/R1 "B", call R3/C1 "C" and call C3 "D". As you are dealing with straight lines, there doesn't seem to be any need to label the middle of the lines.

    Then you have: the ball falls from A to B, it rests from B to C, and it climbs from C to D. You can refer to the periods of time as tAB tBC and tCD.
    Thank you again for your quick reply,

    b=F3 and b=R1, how could I write the relation between F3 and R1 keeping the names F3 and R1?
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  14. #13  
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    Quote Originally Posted by Raspberry red View Post
    b=F3 and b=R1, how could I write the relation between F3 and R1 keeping the names F3 and R1?
    I see no reason you shouldn't use F3 = R1.

    The notation on your diagram was confusing because I thought you were saying that (F1->F2->F3) was equal to (R1->R2->R3).
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  15. #14  
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    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Raspberry red View Post
    b=F3 and b=R1, how could I write the relation between F3 and R1 keeping the names F3 and R1?
    I see no reason you shouldn't use F3 = R1.

    The notation on your diagram was confusing because I thought you were saying that (F1->F2->F3) was equal to (R1->R2->R3).
    Thank you Strange,

    I understand what you thought. Would it be less confusing if I write it like this:
    T1-->T2-->(T3 = R1)--> R2-->R3 for example?
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  16. #15  
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    Quote Originally Posted by Raspberry red View Post
    I understand what you thought. Would it be less confusing if I write it like this:
    T1-->T2-->(T3 = R1)--> R2-->R3 for example?
    Less confusing. But not especially meaningful. Your diagram explains it better.

    What are you trying to do/say with this diagram?
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  17. #16  
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    Quote Originally Posted by Raspberry red View Post
    Quote Originally Posted by Strange View Post
    Quote Originally Posted by Raspberry red View Post
    b=F3 and b=R1, how could I write the relation between F3 and R1 keeping the names F3 and R1?
    I see no reason you shouldn't use F3 = R1.

    The notation on your diagram was confusing because I thought you were saying that (F1->F2->F3) was equal to (R1->R2->R3).
    Thank you Strange,

    I understand what you thought. Would it be less confusing if I write it like this:
    T1-->T2-->(T3 = R1)--> R2-->R3 for example?
    Hello Strange,

    With this diagram I am trying to represent a bounce (like a bounce of a ball).
    I would like to represent the first point when the object is falling: F1
    then the duration of the fall: F2
    and the last point of falling: F3

    Same for the resting state, I would like to represent the first point from which the object is at rest (not falling anymore and not climbing): R1
    then the duration of the resting period: R2
    and the last point of rest: R3

    Likewise for the climbing state,
    the first point of the climbing movement: C1
    then the duration of the climbing: C2
    and the last point of climbing: C3

    Then the object falls again in another bounce...
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  18. #17  
    Brassica oleracea Strange's Avatar
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    It may be confusing to use the same sort of notation for points and times. How about F1 and F2 for the start and end points, and TF for the time?

    And, as far as I know, there is no "rest" in a bounce. But I could be wrong.
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  19. #18  
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    Quote Originally Posted by Strange View Post

    And, as far as I know, there is no "rest" in a bounce. But I could be wrong.
    Are we modeling perfectly elastic points? Or real-world objects? When you bounce a ball, the ball spends a finite amount of time on the floor deforming out of shape and then bouncing up with slightly less energy than it had before.

    Has the OP mentioned what kind of bouncing point we're trying to model?
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  20. #19  
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    Quote Originally Posted by Strange View Post
    It may be confusing to use the same sort of notation for points and times. How about F1 and F2 for the start and end points, and TF for the time?

    And, as far as I know, there is no "rest" in a bounce. But I could be wrong.
    Thank you again for your proposal Strange, for F1, TF , F2.
    What I call the rest of the object bouncing is the time when the object is on the ground: it is neither falling nor climbing, the time of rest could be only some thousandths of second, but this time exists and couldn't be ignored I think.
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    Quote Originally Posted by someguy1 View Post

    Are we modeling perfectly elastic points? Or real-world objects? When you bounce a ball, the ball spends a finite amount of time on the floor deforming out of shape and then bouncing up with slightly less energy than it had before.

    Has the OP mentioned what kind of bouncing point we're trying to model?
    Hello someguy1

    I am trying to find how can I write the finite amount of time the ball spends on the floor deforming before it bounces again. Can you tell me more about elastic points please?
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  22. #21  
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    Quote Originally Posted by Raspberry red View Post
    Quote Originally Posted by someguy1 View Post

    Are we modeling perfectly elastic points? Or real-world objects? When you bounce a ball, the ball spends a finite amount of time on the floor deforming out of shape and then bouncing up with slightly less energy than it had before.

    Has the OP mentioned what kind of bouncing point we're trying to model?
    Hello someguy1

    I am trying to find how can I write the finite amount of time the ball spends on the floor deforming before it bounces again. Can you tell me more about elastic points please?
    Physics is not my strong point, perhaps someone else can help. Here's Wiki on elastic collisions.

    Elastic collision - Wikipedia, the free encyclopedia

    An elastic collision is an idealized collision in which no energy is lost. It's like writing a video game where an object bounces off a wall at the correct angle but loses no energy.

    In real-world collisions it depends on the materials. If you bounce a basketball, the ball hits the floor, compresses a little, expands back into shape, and comes back up ... but with less energy.

    I'm sure that mechanical engineers have equations and formulas that quantify all this.
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  23. #22  
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    Thank you someguy1 for your reply.
    Then, in the case I am exploring, the ball bounces without losing energy, and it spends a finite amount of time on the ground before bouncing again. I would like to find and understand the notation used to describe this kind of situation: when the ball falls from F1 to F3, F2 being the duration of the falling state, then it spends a finite amount of time on the ground "in rest" from R1 to R3, R2 being the duration of the rest, then it bounces again from C1 to C3, C2 being the duration of the "climbing" state.
    Also how could I write the fact when the ball passes from the state of falling (F3) to the state of "resting" (R1) ?
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