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Modeling inherited physiological structures based on hyperbolic numbers.

Sergey V Petoukhov1

  • 1Mechanical Engineering Research Institute of the Russian Academy of Sciences, M. Kharitonievskiy Pereulok, 4, 101990, Moscow, Russia.

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Summary

This study models inherited biological systems using hyperbolic numbers, revealing shared genetic structures and connections to resonance theory. The approach highlights harmonic progressions and means, linking biology to music and aesthetics.

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Area of Science:

  • Mathematics
  • Biology
  • Genetics
  • Physics

Background:

  • Inherited biological systems exhibit complex patterns.
  • Understanding the commonality and interconnections between diverse biosystems is crucial.
  • Existing models may not fully capture the underlying structural relationships.

Purpose of the Study:

  • To model inherited biosystems using multi-dimensional hyperbolic numbers and matrix representations.
  • To uncover hidden structural interconnections among different biosystems.
  • To explore the link between biological systems, resonance theory, and mathematical formalisms.

Main Methods:

  • Application of multi-dimensional hyperbolic numbers and their matrix representations.
  • Modeling of phyllotaxis sequences, Mendelian genetics (Punnet squares), and the Weber-Fechner law.
  • Analysis of structural commonalities related to harmonic progressions and means.

Main Results:

  • Identified hidden structural interconnections among diverse inherited biosystems.
  • Demonstrated a commonality in genetic basis across different biological models.
  • Revealed connections between biosystems, resonance theory, and harmonic progressions (1/n, harmonic mean).

Conclusions:

  • Hyperbolic number modeling provides a unified framework for understanding diverse biosystems.
  • Structural commonality in biosystems is linked to harmonic principles found in nature, art, and music.
  • This approach bridges mathematical sciences and biology, fostering mutual enrichment.