Dlanod is building huts, again!
Dlanod the greedy developer is still dreaming of buying a square plot of land on a tropical island and building some vacation huts on in, circular as viewed from above, each with a diameter of six meters. He has not given up on his plan to build them wall-to-wall, although this might be a bit inconvenient for the unfortunate tourists who will have to stay there. Dlanod's chief architect, who went to Yale, advises him that, regardless of the details of the arrangement, he will have to buy at least square meters of land for each hut. Dlanod states that "his intuition" tells him otherwise, and he will be able to do better. Who is right?
Arguing "from first principles," prove the architect's claim, or provide a detailed plan for an arrangement (including the number of huts and the size of the plot) that proves the architect wrong.
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1 solution
D l a n o d i s r i g h t , of course: He can build one hut on 3 6 < 1 4 4 square meters. The architect made a silly error, confusing "diameter" with "radius." ;)