The e Number

The e number.

1. When did number e come into mathematics?
=The number e first comes into mathematics in a very minor way. This was in 1618 when, in an appendix to Napier's work onlogarithms, a table appeared giving the natural logarithms of various numbers.

2. What happened in 1647 with Saint-Vincent and the e number?
=He computed the area under a rectangular hyperbola.Whether he recognised the connection with logarithms is open to debate, and even if he did there was little reason for him to come across the number e explicitly.

3. Write about Huggens and hisstudies back in 1647 and 1661.
=He examined explicitly the relation between the area under the rectangular hyperbola yx = 1 and the logarithm.

4. While Jacob Bernoully was studying acompound interest problem he…..
=He tried to find the limit of (1 + 1/n)n as n tends to infinity. He used the binomial theorem to show that the limit had to lie between 2 and 3 so we couldconsider this to be the first approximation found to e.

5. At last, who was the first to name the e number (using the notation b)?
=As far as we know the first time the number e appears in itsown right is in 1690. In that year Leibniz wrote a letter to Huygens and in this he used the notation b for what we now call e.

6. What was the most interesting fact in this essay?
=ThatEuler did a lot of research and he actually named other numbers like “a” in his works. Also the fact that he calculated the value himself is very interesting because he could exactly put his number anddo a lot of things and calculations with it, including how to expand e.

7. Add more questions and answers…

8. How many places has the approximation for e?
=18 places

9. Whichformula did Euler use to make a connection between sine and cosine =functions and the complex exponential function?
Euler deduced that using De Moivre's formula.

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