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What is the minimum number of items we need to place in an area of 10000m2 and a distance of 5 meters with the whole area covered?

Berhanu Abebe Dagnaw
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  • It depends on what the items are. It could anywhere from one to infinitely many. You'll need to better explain what you want. – CyclotomicField Jan 26 '20 at 15:44
  • So you want to cover the region with radius-5 circles. Are we allowed to determine the shape of the region, or is it maybe a square of side length 100? – RobPratt Jan 26 '20 at 15:44
  • @RobPratt he didn't mention circles. – CyclotomicField Jan 26 '20 at 15:46
  • The shape of the region doesn't really matter, but the maximum distance between the items shouldn't be greater than 5 meters [or exactly 5 meters to make it easier] – Berhanu Abebe Dagnaw Jan 26 '20 at 15:48
  • Is this your question ? – almagest Jan 26 '20 at 16:19
  • Then you might do best if the overall region to be covered is a circle: https://www2.stetson.edu/~efriedma/circovcir/ – RobPratt Jan 26 '20 at 17:09
  • @almagest I don't think so no. Let me explain the question again with more detail.
    Given an area of interest A with surface |A| 10,000 m2, assume we deploy wireless sensor motes with communication range 5 [metres]; the motes are deployed over the area uniformly at random and independently from each other. What is the minimum number of sensors we need to deploy in order to establish a connected wireless sensor network with high probability?     – Berhanu Abebe Dagnaw Jan 26 '20 at 18:56

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