The Day of the Number e

Day of the Number Pi, Pythagoras Theorem Day... The Day of the Number  𝑒 

Let's assign a day to the number e, oh well, why not 😀 Not one, let's assign it two days! That's right! You have heard it well. Depending on where you are from, and hence in which format you are writing the date, we can distinguish two such days.

Some mathematicians, (including me 😀) in order to promote and popularize math, have taken the next two days as a Day of Number e:

 27th of  January or 27.01

European format DD.MM.YYYY 

7th of February or 02.07 

North America's format MM.DD.YYYY

Its first decimals are  2. 71828 18284 59045 23536 02874 71352 66249 77572 47093 69999 95749 66967 62772 40766 30353 54759 45713 82178 52516 64274 .... (these are 'JUST" the first 100), and if you want to check more of them, click here here for the first 10,000.

The number е, is irrational, that said, it can not be represented in a format of a fraction. However, it can be placed in the same sort of a basket 😀  with the number pi. Named Euler's number or Napier's constant (both very cool math guys) the number is transcendental, meaning that is not the root of any polynomial equation with integer coefficients. 

The number itself is vital for too many mathematical concepts.

Firstly, I would bring out the logarithms and where you have them you have the exponents the compound interest, calculus, a bunch of limits, integrals, differentials, etc. My dear readers, this is just a scratch form the math applications of the number 𝑒 . Each of them, contributes their own into the math-related fields, like chemistry, physics, economics. 

How was this number discovered? 

• We can get the number 𝑒 as a limit of a sequence of more than one general terms, and some of them are :   
  

• Number 𝑒 can be represented as a sum of more infinite series, including 
  
  
  
  
              
• The are bounded with the graph of the function  𝑦 = 1/𝓍 land the lines 𝓍 = 1 and 𝓍 = 𝑒 , has area with exactly one unit. 

Of course, there are lots of more ways of interpreting this number, and representing, but for the sake of this vlog and my modest teacher life I will stop here 😀 I am warmly recommending to immerse yourself in a further reading on this Number-e-Day topic.

And, one more thing, one of the upper given 100 digits is incorrect. Oops, yes 😀 For the ones that are into challenges, try to find the incorrect numeral. Good luck!