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Math Help - Venn diagram tool

  1. #1
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    Venn diagram tool

    Hi,
    First off, apologies if this is the wrong forum or even the wrong site...
    This is a geometry question - but I haven't a clue..

    What I'm trying to do is use MS Excel (2003) visual basic to display a 2 circle Venn diagram based on certain facts.

    Facts are:
    Population 1 (Area of circle 1)
    Population 2 (Area of circle 2)
    Intersect (n of Population 2 also in Population 1)

    I'm struggling with calculating the distance between the center of each circle based on the Intersect.

    Eg.
    Pop 1 = 100
    Pop 2 = 200
    Intersect = 50


    Many thanks for any assistance
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  2. #2
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    Venn diagram

    Hello justinbentley1
    Quote Originally Posted by justinbentley1 View Post
    Hi,
    First off, apologies if this is the wrong forum or even the wrong site...
    This is a geometry question - but I haven't a clue..

    What I'm trying to do is use MS Excel (2003) visual basic to display a 2 circle Venn diagram based on certain facts.

    Facts are:
    Population 1 (Area of circle 1)
    Population 2 (Area of circle 2)
    Intersect (n of Population 2 also in Population 1)

    I'm struggling with calculating the distance between the center of each circle based on the Intersect.

    Eg.
    Pop 1 = 100
    Pop 2 = 200
    Intersect = 50


    Many thanks for any assistance
    You don't say why you need to draw this diagram using VBA in Excel. I presume that you want to make it interactive in some way, rather than simply using the drawing tools to create a fixed diagram on the spreadsheet.

    But my question is: what has the number of elements in the intersection of the two sets to do with the distance between the centres of the circles? The answer really is: nothing at all. The circles (and they don't actually need to be circles; ellipses will do just as well) can be fixed in size and position, and any number of elements can be written in each of the four regions in the diagram - the regions denoted in set notation by A - B, B- A, A \cap B and (A \cup B)'

    Am I missing something here, or is that all OK?

    Grandad
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  3. #3
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    Hi,
    Thanks for the reply,

    I'm trying to make the size of the circles representative of the population sizes.
    Working from 3 variables - Population 1 (Circle 1), Population 2 (Circle 2) and the intercept.

    I'm using VBA to draw the cicles, add labels, %'ages etc. Also allows me to plug in new variables and redraw the diagram.

    The diagrams will be proportionally correct, which I need for presentations.

    Thanks again
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  4. #4
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    Hello justinbentley1

    I assume that you want the area of each part of the diagram to be proportional to the numbers it represents. So if you call the radii of the two circles r_1, r_2 and their areas A_1, A_2, obviously

    A_1 = \pi r_1^2, A_2 = \pi r_2^2

    Suppose the centres of the circles are A, B and the circles meet at points C, D; let AB = d, \angle CAB = \theta, \angle CBA = \phi. (Angles in radians.) Then, using the Cosine Rule on triangle ABC:

     \cos \theta = \frac{d^2 + r_1^2 - r_2^2}{2r_1d}

     \cos \phi = \frac{d^2 + r_2^2 - r_1^2}{2r_2d}

    The intersection area is \frac{A_1\theta+A_2\phi}{\pi}-\tfrac12r_1^2\sin 2\theta - \tfrac12r_2^2\sin 2\phi

    You won't be able to find an explicit formula for the distance, d, between the centres - the best I can suggest is that you use an iterative method to find the closest value. Since you'll presumably be working in integers, you could set up a loop with values of i from |r_1-r_2| to r_1 + r_2. You'll have to make sure that if r_1 = r_2 you avoid a division by zero error. Calculate the areas for each value of i, and when the intersection area is closest to the one required, set d = i.

    I attach an Excel 2000 file with some code that works reasonably well. I have assumed that r_1 \ge r_2.

    I hope you can get it to work OK.

    Grandad
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