Euler's number: a new experimental estimation

Abstract

Euler's number e is one of the most well-known integers in mathematics. The base of the natural logarithm is represented by the number e, often known as Neper's number in books. In the work of distinguished mathematician and physicist Jacob Bernoulli, the number e appears as the limit value of a number sequence that Bernoulli studied dealing with the issue of interest. Although it was primarily used for financial calculations. This remarkable number quickly began to be applied in a wide range of natural phenomena and scientific laws of physics, biology, chemistry.  Students in high schools who are nearing the end of their schooling are taught that  is equal to the number e=2.718... This study reports on a new experiment in physics using communicating vessels, where number e appears indirectly. For example, if in described experiment, a vessel with an area of 100 cm² is divided into N=100 smaller vessels with an area of ​​1 cm², we will theoretically reproduce the number e with an accuracy of 0.5%. It is also emphasized that Euler's number is currently used more frequently and may be found in a wide range of scientific fields as well as daily life.