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Is it possible to evenly spaced out objects?

  1. Feb 13, 2016 #1
    I can't figure this out. I mean like all the objects(lets take them as a point mass) must be equally spaced from each. The surrounding nearest point masses from each point mass must be equally separated from that point mass. Square grid doesn't work as 4 out of the 8 closest neighbours are separated from the center diagonally, which is longer than the other 4 that are separated horizontally and vertically. I was thinking grid whereby the squares are replaced by circles by I can't seems to figure out. Is there such a thing?

    Something like this except the circles are connected and not separated as shown above.
  2. jcsd
  3. Feb 13, 2016 #2


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  4. Feb 13, 2016 #3
    Given this and your previous thread you might like to do some background study on packing problems.
  5. Feb 13, 2016 #4
    Thanks! I will look into that.
  6. Feb 13, 2016 #5


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    Think of which triangles tessellate the most evenly.
  7. Feb 14, 2016 #6


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    Bees use hexagons...
  8. Feb 14, 2016 #7


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    ...with their centers laid out in a pattern of equilateral triangles.
  9. Feb 16, 2016 #8
    You seem to have some unusual definition of closest neighbors. With the usual definition, in the square lattice each point has 4 closest neighbors (or nearest neighbors). The points on the diagonal are next-nearest neighbors.
    No matter what the geometry, you will always have next-nearest and next-next-nearest neighbors and so on, which will be at distances larger that the nearest-neighbor distance. Even in triangular or hexagonal lattice.
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