Beauty of Euler number

Euler number e is so beautiful. It changed our world by 25%.

And given below are two expressions which say by themselves why e(Euler number) is so beautiful.

When the 2^m term is in denominator root of e is obtained. When 2^m is in numerator e squared is obtained. 

Here are the screenshots.

It is a great honor that I had approximate expressions with 2 in numerator for squared of five consecutive numbers and with 2 in the denominator for square root of five consecutive numbers.

This is what I am talking about.

So Euler number and my expressions have similar property.

Euler you were the greatest !!

Have a nice day, dear blog readers !!