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Math Help - What chart or diagrams hould I use to illustrate this?

  1. #1
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    What chart or diagrams hould I use to illustrate this?

    I am not sure that this is exactly statistics related question, but bear with me...

    I need to graphically illustrate relations between different dance steps. Each step has two independent parameters: foot rotation in degrees and foot flexion(bending in ankle) in degrees.

    So for example data would:

    step a - foot r. 50, foot f. 25
    step b - foot r. 34, foot f. 31
    step c - foot r. -21, foot f. 0
    step d - foot r. 0 , foot f.10
    etc.

    I thought that I could use coordinate system with x being rotation and y flexion. Is it kind of scatter plot? Maybe some other type of chart or diagram?
    Also some of steps might have range of values rather then exact value like step c could have foot rotation from -21 to -5 degrees. If possible I would like to demonstrate that in my diagram. Kind of like bubble chart, just with bubble size demonstrating range rather then third variable. Maybe somekind of radar chart?
    This will be used only as an illustration of how all types of steps differ just by two parameters; this is not for study or calculations.

    Thanks for the help in advance.
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  2. #2
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    Re: What chart or diagrams hould I use to illustrate this?

    Quote Originally Posted by mathquestion View Post
    I am not sure that this is exactly statistics related question, but bear with me...

    I need to graphically illustrate relations between different dance steps. Each step has two independent parameters: foot rotation in degrees and foot flexion(bending in ankle) in degrees.

    So for example data would:

    step a - foot r. 50, foot f. 25
    step b - foot r. 34, foot f. 31
    step c - foot r. -21, foot f. 0
    step d - foot r. 0 , foot f.10
    etc.

    I thought that I could use coordinate system with x being rotation and y flexion. Is it kind of scatter plot? Maybe some other type of chart or diagram?
    Also some of steps might have range of values rather then exact value like step c could have foot rotation from -21 to -5 degrees. If possible I would like to demonstrate that in my diagram. Kind of like bubble chart, just with bubble size demonstrating range rather then third variable. Maybe somekind of radar chart?
    This will be used only as an illustration of how all types of steps differ just by two parameters; this is not for study or calculations.

    Thanks for the help in advance.
    What format for display you choose depends on what message you are trying to send to your audience. Why is it important that dance steps only have 2 parameters? If you could show that dance steps tend to form clusters in parameter space does that support what you're trying to say? Does it refute it?

    Give us a better idea of what you're trying to demonstrate.
    Thanks from mathquestion
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  3. #3
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    Re: What chart or diagrams hould I use to illustrate this?

    It isn't that much of the choice to have only two parameters, rather then physical reality of this particular dance where only degree of rotation and flexion of the foot are varied and matters. Essentially I want to demonstrate that all the different steps stem from different degrees of only those two motions(parameters). They might look different on outside, yet essentially they are part of same continuity. I want to demonstrate how some steps might end up being others if dancer doesn't pay attention to technique and over/under rotate or over/under flex the foot and how other steps are more different/ ''further away''.
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    Re: What chart or diagrams hould I use to illustrate this?

    Quote Originally Posted by mathquestion View Post
    It isn't that much of the choice to have only two parameters, rather then physical reality of this particular dance where only degree of rotation and flexion of the foot are varied and matters. Essentially I want to demonstrate that all the different steps stem from different degrees of only those two motions(parameters). They might look different on outside, yet essentially they are part of same continuity. I want to demonstrate how some steps might end up being others if dancer doesn't pay attention to technique and over/under rotate or over/under flex the foot and how other steps are more different/ ''further away''.
    Then what you really need to do is have data from a larger set of parameters and demonstrate that the steps all cluster about points in parameter space such that only 2 degrees of freedom are really left. These would correspond with your rotation and flexion angles.

    With a standard 3D perspective you can show a scatter plot for 3 parameters.

    I would show, possibly on the same plot using color, the scatter of (parm1, rotation, flexion) and (parm2, rotation, flexion) where parm1 and parm2 are some other possible parameters of a dance step that you are trying to show actually remain constant.
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  5. #5
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    Re: What chart or diagrams hould I use to illustrate this?

    I would be tempted to show the different steps as different colored "hitboxes" in polar coordinates. From your description, I would assign the radius parameter (r) to the amount of flexion (since it's "unidirectional") and the angle parameter (theta) to the rotation.

    Your "hitboxes" will look like "slices" (wedges) of a donut, that is to say a trapezoid with two parallel curved edges. The "size" of each hitbox would reflect to some degree the range of tolerance in your two variables. One dance step turning into another would thus be clearly shown as two hitboxes overlapping, whereas "clearly distinct" moves would be thus separated by empty space in-between. The center of each hitbox would thus be "ideal execution".

    Using theta as the rotation means that you can show left-foot/right foot symmetry as equal, but opposite angles. This is similar to your "radar chart" idea.

    Just my two cents' worth. Good luck, what a fascinating approach to dancing!
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  6. #6
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    Re: What chart or diagrams hould I use to illustrate this?

    Quote Originally Posted by romsek View Post
    Then what you really need to do is have data from a larger set of parameters and demonstrate that the steps all cluster about points in parameter space such that only 2 degrees of freedom are really left. These would correspond with your rotation and flexion angles.With a standard 3D perspective you can show a scatter plot for 3 parameters.I would show, possibly on the same plot using color, the scatter of (parm1, rotation, flexion) and (parm2, rotation, flexion) where parm1 and parm2 are some other possible parameters of a dance step that you are trying to show actually remain constant.
    I am statistics noob, sorry. Shouldn't I be able to use only 2D scatter plot, since there is no 3rd parameter? I'm probably messing up the terms. I want to compare steps within 2 parameters and that way show that some steps are closer to each other in its properties while others are more different, yet still ''made of same parametrs''.
    For example step a is a 50 degree foot rotation and a 25 degree foot flexion.
    Step b is a 40 degree foot rotation and 20 degree foot flexion.
    Step c is 10 degree foot rotation and 20 degree foot flexion.
    If I would use 2d coordinate system, wouldn't it illustrate that a is much closer to b then to c. Does it make any sense? Sorry for butchering math terms
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  7. #7
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    Re: What chart or diagrams hould I use to illustrate this?

    well if you only have data on the two parameters you won't be able to demonstrate your hypothesis that those are the only two effective parameters that describe a given dance step.

    If you just want to plot those two parameters against each other then sure a 2D scatter plot will do it but I'm not sure what it will tell you.
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