what is the value of e ? Who discovered this e ?

Answer 1

e = 2.71828 18284 59045 23536...
According to wikipedia, Leonhard Euler started to use the letter e for the constant in 1727, but the constant itself was used before that by Gottfried Leibniz and William Oughtred/ John Napier.

Answer 2

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What is e? Who first used e? How do you find it? How many digits does it have?


e = 2.71828..., the Base of Natural Logarithms

e is a real number constant that appears in some kinds of mathematics problems. Examples of such problems are those involving growth or decay (including compound interest), the statistical "bell curve," the shape of a hanging cable (or the Gateway Arch in St. Louis), some problems of probability, some counting problems, and even the study of the distribution of prime numbers. It appears in Stirling's Formula for approximating factorials. It also shows up in calculus quite often, wherever you are dealing with either logarithmic or exponential functions. There is also a connection between e and complex numbers, via Euler's Equation.

e is usually defined by the following equation:

e = limn->infinity (1 + 1/n)n.

Its value is approximately 2.718281828459045... and has been calculated to 869,894,101 decimal places by Sebastian Wedeniwski (you'll find the first 50 digits in a Table of constants with 50 decimal places, from the Numbers, constants and computation site, by Xavier Gourdon and Pascal Sebah).

The number e was first studied by the Swiss mathematician Leonhard Euler in the 1720s, although its existence was more or less implied in the work of John Napier, the inventor of logarithms, in 1614. Euler was also the first to use the letter e for it in 1727 (the fact that it is the first letter of his surname is coincidental). As a result, sometimes e is called the Euler Number, the Eulerian Number, or Napier's Constant (but not Euler's Constant).

An effective way to calculate the value of e is not to use the defining equation above, but to use the following infinite sum:

e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ...

If you need K decimal places, compute each term to K+3 decimal places and add them up. You can stop adding after the term 1/n! where n! > 10K+3, because, to K+3 decimal places, the rest of the terms are all zero. Even though there are infinitely many of them, they will not change the decimal places you have already calculated. Now the last decimal place or two of the resulting sum may be off due to truncation or rounding of each term, but the first K places should be correct. That is why the computation uses extra decimal places.

As an example, here is the computation of e to 22 decimal places:

1/0! = 1/1 = 1.0000000000000000000000000
1/1! = 1/1 = 1.0000000000000000000000000
1/2! = 1/2 = 0.5000000000000000000000000
1/3! = 1/6 = 0.1666666666666666666666667
1/4! = 1/24 = 0.0416666666666666666666667
1/5! = 1/120 = 0.0083333333333333333333333
1/6! = 1/720 = 0.0013888888888888888888889
1/7! = 1/5040 = 0.0001984126984126984126984
1/8! = 1/40320 = 0.0000248015873015873015873
1/9! = 1/362880 = 0.0000027557319223985890653
1/10! = 1/3628800 = 0.0000002755731922398589065
1/11! = 0.0000000250521083854417188
1/12! = 0.0000000020876756987868099
1/13! = 0.0000000001605904383682161
1/14! = 0.0000000000114707455977297
1/15! = 0.0000000000007647163731820
1/16! = 0.0000000000000477947733239
1/17! = 0.0000000000000028114572543
1/18! = 0.0000000000000001561920697
1/19! = 0.0000000000000000082206352
1/20! = 0.0000000000000000004110318
1/21! = 0.0000000000000000000195729
1/22! = 0.0000000000000000000008897
1/23! = 0.0000000000000000000000387
1/24! = 0.0000000000000000000000016
1/25! = 0.0000000000000000000000001
-----------------------------
2.7182818284590452353602875

Then to 22 decimal places, e = 2.7182818284590452353603, which is correct. (Actually,it's correct to 25 places, but that was luck!).

There have been recent discoveries of even more efficient ways of computing e, one of which was used for setting the record mentioned above.

It is a fact (proved by Euler) that e is an irrational number, so its decimal expansion never terminates, nor is it eventually periodic. Thus no matter how many digits in the expansion of e you know, the only way to predict the next one is to compute e using the method above using

Answer 3

The value of e cannot be expressed as a finite sequence of digits, but it's about
2.7182818284590452353602874713527.

e, Euler's number, was widely publicised by Leonhard Euler, but he cannot take credit for it.

Its importance was first beheld on trying to differentiate the logarithmic function:
y = log_a [x]
y+ ~y = log_a [x + ~x] [using ~ as delta]
~y = log_a [(x + ~x)/x]
~y/~x = {log_a [1 + (~x)/x]}/~x
=y / log_a { [1 + (~x)/x] ^[x/~x]}. If we let the number x/~x = n then this n will be arbitrarily large. If we call the value in the expression e,
we get
dy/dx = y / log_a [e] = y log_e [a].
Hence the inverse of the logarithm to base e, the exponential function with base e, has a rate of increase that is equal to itself.

If you sent a bunch of letters out to a bunch of people, the chance that they all reach the wrong person approaches 1/e as you send out more letters.

It is connected to other important constants by the famous equation
e^[i * pi] = -1.

Answer 4

The word ''e'' is also defined as Eccentricity.
In mathematics, eccentricity is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.

In particular,

1) The eccentricity of a circle is zero.
2) The eccentricity of an (non-circle) ellipse is greater than zero and less than 1.
3) The eccentricity of a parabola is 1.
4) The eccentricity of a hyperbola is greater than 1 and less than infinity.
5) The eccentricity of a straight line is 1 or ∞, depending on the definition used.


For eccentricity of an ellipse go to http://en.wikipedia.org/wiki/Image:Ellipse.png

For hyperbola go to http://en.wikipedia.org/wiki/Eccentricity_%28mathematics%29#Hyperbola

For straight lines go to http://en.wikipedia.org/wiki/Eccentricity_%28mathematics%29#Straight_line

Answer 5

e = 2.71828..... It is the base for all natural logarithms.

e is usually defined by the following equation:
e = lim n->infinity (1 + 1/n)n.

The number e was first studied by Leonhard Euler in the 1720s, but other scientists alluded to it in earlier work.

Answer 6

e = 2.71828183
The first indication of e as a constant was discovered by Jacob Bernoulli

Answer 7

It's about 2.718281828 and is defined as the limit, as n goes to infinity, of (1 + 1/n)^n.

The letter stands for Euler's name, as it is Euler's constant.

Answer 8

2.71828183, except its irrational and goes on forever.
It really is considered to be a nature-like constant, the golden ratio, i believe it was discovered by the Greeks

Answer 9

The value of e is 2.718281828
Euler devised this value.

Answer 10

the value of e is 2.7(approx)
it was discovered by JHON NAPIER