### **Euler's number (e)**

Among mathematicians, *e *is considered to be one of the most important numbers in mathematics, along with pi (p), *i *(Ö-1), 0 and 1, all of which are linked to the famous and mysterious Euler Identity, *e*ip + 1 = 0. Moreover, e appears at the core of several important areas of modern mathematics including calculus.

The numerical value of *e* truncated to 50 decimal places is 2.7182818284590452 3536028747135266 249775724 709369995…..

Scottish theologian and mathematician John Napier (1550-1617), while trying to simplify multiplication by finding a model which transforms multiplication into addition, came up with the idea of logarithm. The model is almost equivalent to what we know as logarithm today.

Napier created first table of logarithms in 1614 and used a number close to 1/*e* as the base, although Napier’s definition did not use bases or algebraic equations. Algebra was not advanced enough in Napier’s time to allow such definition. Logarithmic tables were constructed; even tables very close to natural logarithmic tables, but the base, ‘*e*’ did not make a direct appearance till about a hundred years later. Gottfried Leibniz (1646-1716), in his work on calculus, identified ‘*e*’ as a constant, but labelled it ‘*b*’.

As with many other concepts, it was Leonhard Euler (1707-1783) who gave the constant its letter designation, ‘*e*’, and discovered many of its remarkable properties. Euler’s discoveries cast new light on the previous work, bringing out *e*’s relevance to a host of result and applications.

During sixteenth century it was also noticed that the expression (1+1/n)n appearing in the formula for compound interest tends to a certain limit – about 2.71828 as n increases.

The value (1+1/n)n approaches ‘*e*’ as n gets bigger and bigger:

The first 10-digit prime in ‘*e*’ is 7427466391, which starts as late as at the 99th digit.