Symmetry in motion in euler's formula and its breakdown in hyperbolic function and growth function

Masataka Shimojo

研究成果: Contribution to journalArticle査読

6 被引用数 (Scopus)

抄録

This study was designed to investigate the symmetry in motion in Euler's formula and its breakdown in hyperbolic function and growth function. The results obtained were as follows. (1) The symmetry in motion between θ and exp(iθ) was shown when θ was kept in motion. The symmetry breakdown in motion between θ and cosh(θ), between θ and sinh(θ), and between θ and exp(θ) was shown when θ was kept in motion. (2) There were some properties that were common to these three functions. (3) If hyperbolic function related exponential function with Lorentz transformation, then the Bondi-k factor was an exponential function. (4) Mathematical relationships between the Bondi-k factor and the imaginary unit were suggested. (5) Mathematical relationships between Euler's formula and growth function were discussed by relating qualitative differences in complex numbers with quantitative differences in real numbers. It was suggested that the breakdown of symmetry in motion in Euler's formula gave hyperbolic function and growth function, where some properties common to these three functions were also observed.

本文言語英語
ページ(範囲)79-81
ページ数3
ジャーナルJournal of the Faculty of Agriculture, Kyushu University
56
1
出版ステータス出版済み - 2 2011

All Science Journal Classification (ASJC) codes

  • Agronomy and Crop Science
  • Biotechnology

フィンガープリント 「Symmetry in motion in euler's formula and its breakdown in hyperbolic function and growth function」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル