Derivation of epsilon (e) and pi (Π) from the kinetic molecular theory of matter

Abstract

This paper considers the possible physical origins of the important natural constants epsilon (e = 2.7182') and pi (π = 3.1415'). They are suggested to originate from the kinetic molecular nature of matter. Epsilon (e) is suggested to be the ratio of the driving force on a randomly moving particle accelerated with a quantum of energy, for instance thermal action (kT), in a specified direction to the restoring force acting in the opposite direction. Pi (π), on the other hand, is suggested to be the ratio of the sum of all the other forces pulling the particle in different directions, towards random motion, to the driving force in the direction of acceleration. The paper proposes new methods for the estimation of these parameters from physical first principles.

KEYWORDS: kinetic molecular, epsilon, pi, random motion, natural constants, quantum of energy.