Euler number
There are several famous and widely used irrational numbers. We might be familiar with the most popular number pi; but what about the number e?
So, Let's start with...
e = 2.7182818284590452353602874713527...
Why Euler number?
The number e is called Euler's Number because it was first used by Leonhard Euler in the 1700s.. However, another mathematician named John Napier used the number back in the 1600s with logarithms. Napier just didn't call it e yet.
It is equal to the base of the natural logarithm.
ln x = log e(x)
Let's approximate Euler number 🤜🤛
Euler's number is irrational, which means that the decimal never terminates or ends, and it does not repeat. The digits after the decimal continue indefinitely. That means that it is impossible to write an exact value to represent e, but there are some expressions that are approximate values of e.
One possible way to approximate the value of e is:
There are another ways to do this.
One of them is to use the expression (1 + 1/n) ^n ; as the value of n increases, the expression becomes closer and closer to the value of e .
What Euler number gives us?✍️
The number , becomes helpful in many different mathematical situations, like determining the compounded interest on continuously compounded bank accounts. In fact, this very use of the value of e is how Euler came up with the number.
Once you get deeper into your maths journey, you will find that e turns up everywhere! Euler's number is especially helpful in engineering, probability and trigonometry applications. For example, it is used in Newton's heating and cooling, it is used to relate trigonometric functions to hyperbolic functions, it is used in probability to represent the normal distribution and it is even used in calculations with electric circuits!
The 100 decimal digits of Euler number e 🤔
182845904523536028747135266249775724709369995957
9676277240766303535475945713821785251664274...
Let's end up e with the most amazing equation:
.
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