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Math Help - Counting the number of equally spaced points in a given area

  1. #1
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    Counting the number of equally spaced points in a given area

    Hi, I got a problem that I cannot get my head around, here it is:

    I am given an area of xxx m2

    The task is to count the number of equally spaced points within that area

    The spacing between each point is given and arranged in the following pattern
    Counting the number of equally spaced points in a given area-ex.jpg

    Note that there may be millionbs of points in that huge area

    Thanks so much for any advice
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kcmei View Post
    Hi, I got a problem that I cannot get my head around, here it is:

    I am given an area of xxx m2

    The task is to count the number of equally spaced points within that area

    The spacing between each point is given and arranged in the following pattern
    Click image for larger version. 

Name:	ex.JPG 
Views:	37 
Size:	3.7 KB 
ID:	21092

    Note that there may be millionbs of points in that huge area

    Thanks so much for any advice
    There is no simple formula for this without knowing something about the shape of the area. But there could be approximately [xxx/(1.2)^2](2/sqrt(3))

    Each triangle has three vertices and each vertex is a vertex of six triangles. So if the area of a triangle is A there are approximately xxx/A triangles and so (xxx/A)*2 points.

    CB
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