Packing problem regarding a disc

115 Views Asked by At

Suppose that there is a packing of 1000 unit discs in the rectangle R. It means that these 1000 discs lie inside of R and any two of them do not share a common interior point (but they could touch each other). Prove that there is a packing of 4000 discs of diameter 1 in R. The mentioned problem is related to the packing problem. I am very new to this idea. I am trying to find some relevant material but I am unable to find any proper notes or website. I found this https://en.wikipedia.org/wiki/Circle_packing_in_a_square but I guess it's different from what I am trying to solve. If anyone can suggest some good websites it will be really helpful also.

1

There are 1 best solutions below

0
On BEST ANSWER

A rectangle $R$ with width $w$ and height $h$ can be divided into $4$ rectangles of width $\frac w2$ and height $\frac h2$.