What is e?

Answer 1

The mathematical constant e is the base of the natural logarithm. It is occasionally called Euler's number after the Swiss mathematician Leonhard Euler, or Napier's constant in honor of the Scottish mathematician John Napier who introduced logarithms. (e is not to be confused with γ – the Euler–Mascheroni constant, sometimes called simply Euler's constant.) The number e is one of the most important numbers in mathematics, alongside the additive and multiplicative identities 0 and 1, the imaginary unit i, and π, the circumference to diameter ratio for any circle in a plane. It has a number of equivalent definitions. Since e is transcendental, and therefore irrational, its value cannot be given exactly as a finite or eventually repeating decimal or continued fraction. The numerical value of e truncated to 20 decimal places is:

2.71828 18284 59045 23536...

Answer 2

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4696027662583 599051 9870423 001 7946553 679

Answer 3

lower case e:

It refers to Euler's constant, which is irrational (it extends forever without repeating), and is about
2.718281828459045235360287471352662497757247093699959574966
(this page has the first 5,000,000 digits: http://antwrp.gsfc.nasa.gov/htmltest/gifcity/e.5mil )

It has many interesting and important properties:

(1) It is the base of the natural logarithm, ln, which is the preferred base since it can be easily manipulated in calculus and higher level math (its derivative is 1/x)

(2) The derivative of e^x is always e^x

(3) It is transcendental, which means that there is no polynomial with rational coefficients whose solution could be e. In other words, e can never be the zero of a polynomial that doesn't have another irrational number in it already.

(4) If you take the sum:
1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! + .... + 1/n! + ...
and keep going till n is infinity, you get e. (Prove this by finding the Maclaurin series of e^x and plugging in 1)

(5) the limit of (1+1/n)^n as n goes to infinity is e.

(6) e^(i x) = cos x + i sin x (where i = √(-1))

The list goes on and on....

Try googling "Euler's number" to find more information.


upper-case E:

It stands for energy, and has several equations to represent it:
E = (1/2) m v^2 for kinetic energy of a mass of m moving at a velocity of v
E = mgh for gravitational potential energy of a mass of m a height of h off the ground of a planet with gravity g
E = -(1/2) k x^2 for spring potential energy of a spring with spring constant k stretched x from its original position.
E = mc^2 for the change in energy when m kg is converted into energy

Answer 4

e is a natural number of 2.7. its an expoential in that a number will increase expoentially for infinite and will get to the point where there rate of change between the numbers will arrive at a constant of approxiamatly 2.7 which is known as the natoral number e

Answer 5

On a calculator it is the way to express an error.
But that's probably not what you are referring to. As a mathematical constant it is the "Base of Natural Logarithms"
= 2.71828.... Like Pi it goes on indefinately

Answer 6

"e" is the base of natural logarithms. It can be calculated by:
     n=0
1) ∑ 1/N!
     ∞

OR

2) lim x→∞ (1+1/x)^x

e is used as the symbol in honor of Leonhard Euler.

Answer 7

The fifth letter of the English alphabet.

Answer 8

its a variable that represents a number
i cant remember what it equals, but you can find it on a ti 83 or 84 calculator
its definitely a number

Answer 9

that because you dont know how to enter it in the calculator. e is a neutral number. now any number to the first power is itself. for example, 4^1=4, 3985^1=3985, so e^1=2.71828182846.....

Answer 10

Approximately 2.71828182