J4 ›› 2011, Vol. 38 ›› Issue (3): 1-6.doi: 10.3969/j.issn.1001-2400.2011.03.001

• Original Articles •     Next Articles

N-generation Fibonacci sequence and  the Nth-generation golden section

LIANG Changhong;TAN Kangbo;ZHANG Wei   

  1. (Science and Technology on Antenna and Microwave Lab., Xidian Univ., Xi'an   710071, China)
  • Received:2010-10-14 Online:2011-06-20 Published:2011-07-14
  • Contact: TAN Kangbo E-mail:kbtan@mail.xidian.edu.cn

Abstract:

The Fibonacci Sequence can be seen as the 2-generation symmetrical genetic series, which corresponds to the golden section. It is extended to the Second-generation uneven K&M sequence and the corresponding partition in this paper. The N-generation Fibonacci Sequence and the Nth-generation golden section are proposed. It is specifically pointed out that the Nth-generation (N→∞) golden section is known as the Zhuangzi cutting rod.

Key words: K&M series, the Nth-generation Fibonacci Sequence, the Nth-generation golden section, Zhuangzi cutting rod