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how much of an overhang can you achieve by stacking books on a table [Music] lets assume that each book is one unit long to balance one book on a table the center of gravity of the book must obviously be somewhere over the table to achieve the maximum overhang of a stack of books the center of gravity of the stack should lie directly above the tables edge [Music] the maximum overhang with one book is obviously half a unit for two books the center of gravity of the first book should be directly over the edge of the second and the center of gravity of the stack of the two books should be directly above the edge of the table the centre of gravity of a stack of two books is at the midpoint of the books overlap or one plus a half over two which is three quarters of a unit from the far end of the top book it turns out that the overhangs are related to whats known as the harmonic sequence if there are n books the maximum overhang is one plus a half plus a third plus a quarter all the way