2.718281828

The natural logarithm can be defined for all positive real numbers a as the area under the curve y = 1/x from 1 to a.

This number is irrational, and approximated to 2.718281828...

As already described in the topic of Pi, there is a connection between Pi and natural logarithm. This is because that natural logarithm is utilized for expressing complex number and a vector on the plate by polar form.