Euler's Number () is a constant roughly equal to 2.71828. It frequently appears in mathematics in various fields. It is the base of natural logarithms. The function is graphed below.
The easiest way to describe why is an interesting number worthy of analysis is to view its properties in calculus. When trying to find the slope of the function one only needs to plug in the value of x they want to find the slope at. For example if we want to find the slope at we merely calculate . We can double check using a slope formula with the points to approximate the slope: .
Euler's Number's definition is more in depth than this, this is merely to demonstrate some of it's interesting properties and to show it isn't just a random number.
