Project #161348 - Geometry

I am solving a problem related to this paper http://www.umac.mo/rectors_office/docs/weizhao_cv/pub_refereed_conferences/2015_conferences/07069403.pdf. You only need to read section IV. You could solve my problem without reading other sections. My problem is if I place one node at each vertex of all the hexagons in figure 2 and 3. What's the upper bound and lower bound of the number of the nodes both in arbitrarily shaped area (like figure 2) and rectangle (like figure 3). This section omits some proofs, so I can't understand its proof. I need complete and detailed proof

Subject Mathematics
Due By (Pacific Time) 12/20/2016 10:00 pm
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