Napier's constant, imaginary unit, circular constant and some natural phenomena

Masataka Shimojo, Yutaka Nakano

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This study investigated relationships between some mathematical constants [Napier's constant (e), imaginary unit (i), circular constant (π)] and some natural phenomena. The results obtained were as follows. The equality between exponential function based on e and Bondi K-factor suggested hypotheses that both expressions required each other and exponential function was associated with the space-time continuum. The mathematical application of v → ∞ to Bondi K-factor led to i, where i was interpreted as something other than v due to the definition of v as 0≤v<c (c=speed of light in vacuum). This suggested a hypothesis that the role of i, though the phenomenon related to i looked like the phenomenon related to the infinite velocity, was to prohibit the state of c ≤ v < ∞ by taking the form of wave. Euler's identity was related with Bondi K-factor to the power of i where v=c(exp(2π)-1)/ (exp(2π)+1) - 0.996c (- muon's velocity). Applying v → ∞ to Bondi K-factor to the power of i gave 'i to the power of i, a many-valued function that suggested numeral approximations to some physical constants. Some natural phenomena including metallic number and muon's velocity were related to π. It was suggested that e, i and π were the basso continuo being played in some natural phenomena.

Original languageEnglish
Pages (from-to)281-285
Number of pages5
JournalJournal of the Faculty of Agriculture, Kyushu University
Issue number2
Publication statusPublished - Sept 2013

All Science Journal Classification (ASJC) codes

  • Agronomy and Crop Science
  • Biotechnology


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