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What is e ?
What is e ?
e is an irrational number.
What is e ?
e is an irrational number.
e ≈ 2.718
What is e ?
e is an irrational number.
e ≈ 2.718
e ≈ 2.718281828
What is e ?
e is an irrational number.
e ≈ 2.718
e ≈ 2.718281828
and, the value of e to a
“few” more decimal places :
e≈
Why the letter e ?
Leonhard Euler (lay’-ohn-hart oy’ –lur,)
5/15/1701 to 9/18/1783
was born in Basel, Switzerland.
He was one of the most prolific mathematicians in
history. He refined the notion of a FUNCTION;
made common many mathematical notations
including e , i for 1 , the pi symbol (∏) , and
the sigma symbol (Σ).
How can we compute the value for e?
n
 1
e   1   for n "very large".
 n
1,000,000
1


1

 1, 000, 000 


 2.718280469
1,000,000,000
1


1  1, 000, 000, 000 


 2.718281827
Your calculator shows that e
 2.718281828
How does your calculator
compute the value for e ?

1
1 1 1 1 1
1
e  
    

 ...
1 1 2 6 24 120
k 0 k !
And finally …
e