In mathematics, terms like rational number and rational function are familiar to many. However, the Japanese translations of these terms, 有理数 (“yūrisū”) and 有理函数 (“yūri kansū”), raise an intriguing question: do these translations truly capture the meaning of the English word “rational”?🤔 While “rational” in English mathematically refers to properties involving ratios, the Japanese word…

During my graduate studies, I worked extensively with algebras and their corresponding geometric objects, as outlined below. The symbol “\( \leftrightarrow \)” represents a one-to-one correspondence between isomorphism classes. Key Algebras and Their Geometric Correspondences Properties of Algebras and Their Geometric Significance Although these algebras are computationally challenging, they serve as powerful tools for studying…

The Lotka-Volterra equation is known as a nonlinear differential equation that provides the simplest representation of a predator-prey system between two species without intraspecific competition. This model describes the interaction between prey (the consumed species) and predators (the consuming species), playing a fundamental role in learning the basics of ecological concepts. Basic Structure of the…

When a butterfly🦋 flaps its wings in one place, a tornado🌪️ occurs on the other side of the earth. This is a metaphor for the phenomenon that started chaos theory at the beginning of the movie “The Butterfly Effect,” in which small differences in initial conditions can make a big difference in future outcomes. The…

In the field of dynamical systems, an attractor is the state or destination of convergence of a system over time. In a system called a “dissipative system” in which energy flows in and out, an attractor is the point or state to which the system finally settles, and appears in a fixed form independent of…