“Golygon”的概念、定义、习题解题方法及翻译-数学辞典

单词

Golygon

释义

Golygon

A Plane path on a set of equally spaced Lattice Points, starting at the Origin,where the first step is one unit to the north or south, the second step is two units to the east or west, the third is threeunits to the north or south, etc., and continuing until the Origin is again reached. No crossing or backtrackingis allowed. The simplest golygon is (0, 0), (0, 1), (2, 1), (2, ), (, ), (, ), (, ), (, 0),(0, 0).

A golygon can be formed if there exists an Even Integer such that

			(1)
			(2)

(Vardi 1991). Gardner proved that all golygons are of the form

. The number of golygons of length

(Even), witheach initial direction counted separately, is the Product of the Coefficient of

(3)

with the Coefficient of

(4)

The number of golygons

of length

for the first few

are 4, 112, 8432, 909288, ... (Sloane's A006718)and is asymptotic to

(5)

(Sallows et al. 1991, Vardi 1991).

See also Lattice Path

References

Dudeney, A. K. ``An Odd Journey Along Even Roads Leads to Home in Golygon City.'' Sci. Amer. 263, 118-121, July 1990.

Sallows, L. C. F. ``New Pathways in Serial Isogons.'' Math. Intell. 14, 55-67, 1992.

Sallows, L.; Gardner, M.; Guy, R. K.; and Knuth, D. ``Serial Isogons of 90 Degrees.'' Math Mag. 64, 315-324, 1991.

Sloane, N. J. A. SequenceA006718/M3707in ``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.

Vardi, I. ``American Science.'' §5.3 in Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 90-96, 1991.

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。