“Book Stacking Problem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Book Stacking Problem

释义

Book Stacking Problem

How far can a stack of books protrude over the edge of a table without the stack falling over? It turns out that themaximum overhang possible for books (in terms of book lengths) is half the th partial sum of the HarmonicSeries, given explicitly by

where

is the Digamma Function and

is the Euler-Mascheroni Constant. The first few values are

(Sloane's A001008and A002805).

In order to find the number of stacked books required to obtain book-lengths of overhang, solve the equation for, and take the Ceiling Function. For , 2, ... book-lengths of overhang, 4, 31, 227, 1674, 12367,91380, 675214, 4989191, 36865412, 272400600, ... (Sloane's A014537) books are needed.

References

Dickau, R. M. ``The Book-Stacking Problem.''http://www.prairienet.org/~pops/BookStacking.html.

Eisner, L. ``Leaning Tower of the Physical Review.'' Amer. J. Phys. 27, 121, 1959.

Gardner, M. Martin Gardner's Sixth Book of Mathematical Games from Scientific American. New York: Scribner's, p. 167, 1971.

Graham, R. L.; Knuth, D. E.; and Patashnik, O. Concrete Mathematics: A Foundation for Computer Science. Reading, MA: Addison-Wesley, pp. 272-274, 1990.

Johnson, P. B. ``Leaning Tower of Lire.'' Amer. J. Phys. 23, 240, 1955.

Sharp, R. T. ``Problem 52.'' Pi Mu Epsilon J. 1, 322, 1953.

Sharp, R. T. ``Problem 52.'' Pi Mu Epsilon J. 2, 411, 1954.

Sloane, N. J. A. SequencesA014537,A001008/M2885, andA002805/M1589,in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。