Definition – What is e (Euler’s number or Napier’s constant)?
“e” is a mathematical constant and natural number. The starting digits are 2.7182818284590. It is often called “Euler’s number” or “Napier’s constant.”
e has no end to the number of decimals (similar to the number pi).
e calculates as 1 +( 1÷1 )+ (1÷(1 x 2)) + (1÷(1 x 2 x 3)) + (1÷(1 x 2 x 3 x 4))…. There is a repeating pattern that continues until infinity. The pattern adds fractions of 1 divided by all previous numbers.
Formula – How is e to the exponent calculated?
e to the exponent calculates by multiplying e together the number of times of the exponent.
e3 is e • e • e = 20.0855369
e5 is e • e • e • e • e = 148.413159
Sources and more resources
- A simple introduction to the concept of e from Math is Fun, Wolfram MathWorld, and Popular Mechanics.
- Wikipedia articles on e (mathematical constant), Exponentiation and the Exponential function have more information on the concept of e.
- Kalid Azad’s Better Explained goes into more detail with an Intuitive Guide to Exponential Functions & e.
- NASA has a listing of the first 2 million digits of the number e.
- Robin Wilson of Gresham College details the story of e.