Researches on Mathematical Relationship of Five Elements of Containing Notes and Fibonacci Sequence Modulo 5

TL;DR

This paper explores a mathematical link between traditional Chinese medicine concepts and the Fibonacci sequence modulo 5.

Contribution

The study introduces new number series and arrangements linking TCM's five elements to Fibonacci patterns modulo 5.

Findings

Key number series 12534 and 31542 were derived from Fibonacci sequence modulo 5.

Three new arrangements of the five elements of containing notes correlate with these Fibonacci subsequences.

The findings suggest a novel mathematical basis for traditional Chinese medicine theories.

Abstract

Considering the five periods and six qi's theory in TCM almost shares a common basis of stem-branch system with the five elements of containing notes, studying the principle or mathematical structure behind the five elements of containing notes can surely bring a novel view for the five periods and six qi's researches. By analyzing typical mathematical rules included in He tu, Luo shu, and stem-branch theory in TCM as well as the Fibonacci sequence especially widely existent in the biological world, novel researches are performed on mathematical relationship between the five elements of containing notes and the Fibonacci sequence modulo 5. Enlightened by elementary Yin or Yang number grouping principle of He tu, Luo shu, the 12534 and 31542 key number series of Fibonacci sequence modulo 5 are obtained. And three new arrangements about the five elements of containing notes are then introduced, which have shown close relationship with the two obtained key subsequences of the Fibonacci sequence modulo 5. The novel discovery is quite helpful to recover the scientific secret of the five periods and six qi's theory in TCM as well as that of whole traditional Chinese culture system, but more data is needed to elucidate the TCM theory further.

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