Although likely the most
famous of engineering numbers it is a relatively late comer.
Makes a cameo appearance
in the work of Napier, around 1614 with the advent of logarithms.
Napier was generally regarded to be in league with the
devil as he strode round his castle with a black crow on his shoulder
and a spider in a little cage muttering about the predictions of his
apocalyptic algebra.
1647 Saint-Vincent
computed the area under a rectangular hyperbola. y=1/x.
1668 Nicolaus Mercator
published Logarithmotechnia which contains the series expansion of
log(1+x). In this work Mercator uses the term "natural logarithm".
In 1683 Jacob Bernoulli
looked at the problem of compound interest and, in examining continuous
compound interest, 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 could consider this to be the first approximation found
to e.
1690. In that year
Leibniz wrote a letter to Huygens and in this he used the notation b
for what we now call e.
The notation e for this
number is due to Euler and made its first appearance in a letter Euler
wrote to Goldbach in 1731. He made various discoveries regarding e in the following years, but
it was not until 1748 when Euler published Introductio in Analysin
infinitorum that he gave a full treatment of the ideas surrounding e.
Euler showed that
e = 1 + 1/1! + 1/2! + 1/3! + ...
and that e is the limit
of (1 + 1/n)n as n tends to
infinity.
Euler gave an approximation for e
to 18 decimal places,
e = 2.718281828459045235...
Euler was likely the first to prove that e is irrational.
Hermite proved that e
is not an algebraic number in 1873. (ee
still open)
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