'e' is a unique number with numerical value e = 2.7182818284590.... having infinite number of digits. It is popularly called as Euler's number.
Mnemonic for 'e' upto 6 digits is : By omnibus I traveled to Brooklyn.
In mathematics, next to the omnipresent π, 'e' is an important constant extensively appearing in limits and
derivatives. Like 'π' it is an
irrational number i.e., it cannot be expressed as a ratio of two integers.
Common logarithms have a base of 10. A second type, called
natural or Naperian logarithms, have the constant 'e' as its base. In that context 'e' is called Naperian's constant. But 'e' was named after Leonhard Euler, a Swiss mathematician, physician and astronomer. His contribution to several branches of mathematics such as calculus and graph theory was immense.
Consider the region bounded by a hyperbola (xy = 1), the x-axis, and the vertical lines x = 1 and x = e as shown in the animation. The area between the three equations is one square unit. 'e' is a unique number that exhibits the above property.
There is interesting story behind 'e'. Initially mathematicians tried to integrate (1/x) but failed and concluded it is impossible. To keep things moving they called it log(x) with following conditions:
log1 = 0
loge = 1
To find value of 'e' they have drawn the curve of (1/x) and measured the area under curve from x = 1 and when the area reaches 1 the corresponding value of x = e which is physically measured.