Skip to main content
Log in

Generalized golden sections and a new approach to the geometric definition of a number

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We consider applications of generalized golden sections to the geometric definition of a number and establish new properties of natural numbers that follow from this approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A. P. Stakhov, Introduction to Algorithmic Measurement Theory [in Russian], Sovetskoe Radio, Moscow (1977).

    Google Scholar 

  2. A. P. Stakhov, “The golden section in the measurement theory,” Comput. Math. Appl., 17, No.4–6, 613–638 (1989).

    Google Scholar 

  3. G. Bergman, “A number system with an irrational base,” Math. Mag., No. 31, 98–119 (1957).

    Google Scholar 

  4. A. P. Stakhov, “‘Golden’ section in digital technology,” Avtomat. Vychisl. Tekhn., No. 1, 27–33 (1980).

  5. A. P. Stakhov, Codes of Golden Ratio [in Russian], Radio i Svyaz’, Moscow (1984).

    Google Scholar 

  6. N. N. Vorob’ev, Fibonacci Numbers [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  7. E. V. Hoggat, Fibonacci and Lucas Numbers, Houghton-Mifflin, Palo Alto (1969).

    Google Scholar 

  8. A. P. Stakhov, V. Massingua, and A. A. Sluchenkova, Introduction to Fibonacci Coding and Cryptography, Osnova, Kharkov (1999).

    Google Scholar 

  9. V. M. Chernov and M. V. Pershina, “Fibonacci-Mersenne and Fibonacci-Fermat discrete transforms,” Bol. Inform. Golden Section: Theory Appl., No. 9–10, 25–31 (1999).

  10. A. P. Stakhov and I. S. Tkachenko, “Fibonacci hyperbolic trigonometry,” Dokl. Nats. Akad. Nauk Ukr., Issue 7, 9–14 (1993).

  11. A. P. Stakhov, “A generalization of the Fibonacci Q-matrix,” Dopov. Nats. Akad. Nauk Ukr., No. 9, 46–49 (1999).

  12. A. P. Stakhov, “Brousentsov’s ternary principle, Bergman’s number system and ternary mirror-symmetrical arithmetic,” Comput. J., 45, No.2, 231–236 (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1143–1150, August, 2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stakhov, A.P. Generalized golden sections and a new approach to the geometric definition of a number. Ukr Math J 56, 1362–1370 (2004). https://doi.org/10.1007/s11253-005-0064-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-005-0064-3

Keywords

Navigation