There’s this number e that is approximately 2.718281828. e is a special number because it occurs naturally.
Where? What are some examples of e in nature?
Well, there’s one. 
Sorry, couldn’t resist.
Does this help any?
It doesn’t help me any. I’m sure someone will be by shortly who knows this stuff.
IA Extremely NA mathematician, but IIRC e is simply the number defined so that in calculus, the integral of the function e^x is equal to itself. It’s similar to the way phi is defined to be the number whose square is a unit greater than itself, or pi is the ratio of a circle’s circumference to its diameter.
If you had a bunch of married couples and you divided them into men and women, then randomly assigned the women to the men, the chances of no pairs were properly reunited is 1/e or .367879.
This is probabiloity is accurate to six decimal places whether the number of pairs are ten or ten billion or any number in between.
There is a book called Why Do Buses Travel in Three’s and your question made me try td dig my copy out. I couldn’t find it but if the answers you get here are not up to snuff then check it out and see what it has to say.
Some links:
http://mathforum.org/library/drmath/view/53903.html
And from another forum, “Euler’s number will arise in any process in which the rate of change of a quantity is proportional to the quantity itself. Radioactive decay, Newton’s Law of Cooling, Population Growth models and continuous compounding of interest are a few examples.” – Physics Forum
A catenary curve — the curve adopted by a rope, string, chain, vine, or what have you when it’s suspended from two fixed points — follows the hyperbolic cosine function (cosh), which is essentially the sum of two related exponentials with base e.
There was an extensive thread on the ‘natural’ number e and pi, relating the radius/diameter of a circle to it’s area and circumference. Scan through General Questions for all the answers.
Strinka: Sugest you read “Sticky” #3 in General Questions.
Strinka, spingear is suggesting that a single lower-case letter “e” is not much of a title heading. It not only fails to clearly identify the type of question you are asking, it is remarkably difficult for us to click on when we have been drinking.
I have taken the liberty of expanding the title.
[ /Moderator Mode ]
So you’d frown on the new post I was about to write, entitled “i”? Or how about “•”, my new thread about multiplication notation? Or " ", a query I had on usage of the non-breaking space character in HTML?
Anyway, however terse the “e” title might have been, note that because e[sup]x[/sup] is it’s own derivative and anti-derivative, it’s one of the easiest functions to do calculus with when you have been drinking.
You need Calculus to truly appreciate e. Then you can marvel at facts like
The function e[sup]x[/sup] is its own derivative.
e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + … and
e[sup]x[/sup] = x[sup]0[/sup]/0! + x[sup]1[/sup]/1! + x[sup]2[/sup]/2! + …
e = the limit as n approaches infinity of (1 + 1/n)[sup]n[/sup], and
e[sup]x[/sup] is the limit of (1 + x/n)[sup]n[/sup].
This last fact is why e shows up in the formula for interest compounded continuously (as opposed to a certain number of times per year), as ronincyberpunk noted.
e is used in the formula for the bell-shaped curve that shows the standard normal distribution, or Gaussian distribution, that’s all over the place in Statistics.
spingears, you may be thinking of this thread: Pi – it sure gets around. There’s also What exactly do e, Log and ln mean in math
Not at all. I would smile and chortle with merry delight–as I moved it into the unrecoverable æther.
That’s the one! 
I would assume that either you hadn’t read the forum stickies or had forgotten the contents.
An appreciation of/for natural numbers will require a broader exposure to mathematics than can be covered by post and links on SDMB’s as time and space do not permit.
strinka
Here’s a thread I started about ‘e’.
tomndebb
You think just having ‘e’ was a poor title for a thread?
Geez, I’ve seen a lot worse.
How about those incredibly vague threads that start “Anyone know about this”?
Then clicking on the thread just leads to some inane link:
www.some-inane-link.com
Thank you for fixing the title tomndebb.
And thank you to the various people (wolf_meister, Bytegeist, ronincyberpunk, aahala to name a few) for the informtive answers.
I would ask why e does all this stuff but, I have a feeling that I would need to know calculus to understand the answer and that Thudlow Boink answered that question.
Related anecdote:
While in High School Senior year, I was taking Calculus II. I asked the teacher, “What is e? Where does it come from, what is it used for?”
He couldn’t answer the question. He just didn’t know! :eek:
He couldn’t come up with a use for polar coordinates either. It was a math class from hell. Nice way to treat the advance math program, stupid school district. :rolleyes:
Needless to say, I felt compelled to retake calculus in college.
Peees.
Except in cases where you want to know how much of something or other is left after a certain time period (or how long something’s been around,) and your reference materials tell you the half-life. Sure, you can contort the formula to use e, but if you really wanted to you could contort the formule to use π. Simpler to use
C[sub]final[/sub]=C[sub]orig/sub[sup]time/halflife[/sup]
I asked Dr. Math about Real Life applications of Quadratic Equations. He had to create ahackneyed situation to get a situation.
Despite this thread being a zombie, there’s something I’d like to say: a number of purported instances of “e” in nature are really just instances of exponential growth that someone chose to describe in terms of “e”, but which don’t really have anything to do with the particular numeric value 2.71828… in any significant way. Sure, you can choose to see “e” wherever there’s exponential growth, always rewriting b[sup]t[/sup] into e[sup]ln(b)t[/sup], but I don’t think you should think of it as “There’s this magic number 2.71828… that happens to show up in a lot of disparate contexts for mysterious reasons”. It’s just “Exponential growth shows up a lot (and it’s often conveniently described in terms of its natural logarithm)”.
Speaking of which, nor should ln(b) generally be thought of as fundamentally “The power to raise 2.71828… to to reach b”. I think it’s better (particularly when ln(b) is non-real) thought of as fundamentally “The invariant ratio between the t-derivative of b[sup]t[/sup] and b[sup]t[/sup] itself”. The constant defined by e = ln[sup]-1/sup = 2.71828… doesn’t really have anything to do with it; b = e[sup]whatever[/sup] is just a roundabout notation for describing the rate of growth of b[sup]t[/sup].
In short, it’s exponential growth and its measurement via natural logarithm which are ubiquitous; the particular number whose natural logarithm is 1 is also relevant from time to time, but not nearly as often as it is given credit for. The more general idea of exponential growth is the real star.