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Overhang
2009-09-10
“How far off the edge of the table can we reach by stacking n identical, homogeneous, frictionless blocks of length 1?” is a famous elementary, but nontrivial question pertaining to sequences.
László Leindler recalls in his review of Mike Paterson's and Uri Zwick's
article “Overhang” [Am. Math. Mon. 116, No. 1, 19-44 (2009; Zbl 1168.40001)] that a “classical solution achieves an overhang asymptotic to 1/2 lnn. This solution is widely believed to be optimal.”
“But the authors show that `it is exponentially far from optimality by constructing simple n-block stacks that achieve an overhang of cn1/3, for some constant c>0.'”
“Before proving new theorems they present a detailed survey of the long history of the attractive problem to maximize the overhang. It would be worth to enlist all of the theorems, but now we can recall only the main theorem which gives the precise form of the assertion cited above.” “Theorem. D(n)≥(3n/16)1/3-1/4 for all n, where D(n) denotes the maximum overhang that can be achieved using a balanced stack comprising n blocks of length 1. This excellent paper is highly recommended to experts and laymen, as well. At last we like to mention the beautiful and useful illustrations in 24 figures, and the 22 papers of references.”
