Structural chemistry and the transcendental numbers $\upphi$, e and $\uppi$

Abstract

Certain number theory relations that emerge from considerations of the topological character of several patterns taken from structural chemistry are reviewed. These relations define the products $\hbox {e}\cdot \uppi$ and $\upphi \cdot \hbox {e}$ from topological considerations of the respective structural-types. We further present here an approximate number theory formula for the quotient $\uppi /\upphi$ and for the product $\upphi \cdot \hbox { e}\cdot \hbox { e}\cdot \uppi$ that are derived from the earlier formulas based in structural chemistry.