Random question, for no other reason than quibble pretense. Euler's number on Mathworld and Wiki says that e is because it honors him. Yet, in my math text book, it says it was probably chosen because it is the first letter in the word exponential. Aside from killing two birds with one stone, which is more correct?
"e"was around long before Euler so I would bet its for exponential, if those are the two choices. Also, maybe the person who wrote it had just got pass "d" in his equations and took "e" as the next letter.
Since Euler (pronounced OY-ler) himself is the first person to use e as the symbol for that number, we'd have to assume that he was very conceited to have chosen it simply because it's his own initial. I can't find an etymology of the symbol--although I'm hardly a professional scholar so there are whole libraries that I don't have access to. Considering that we do indeed call it "Euler's number," it's quite possible that the notion that e stands for "Euler" is merely a folk-etymology. Its true origin will probably never be known. It had previously been represented by both b and c. Euler was such a giant that in addition to Euler's number there is an entire mathematical glossary of things named after him, including Euler angles, Euler approximation, Euler's conjecture, Euler's criterion, Euler's first and second laws, several different formulas named Euler's formula, Euler's identity, Eulerian integers, Euler polynomials, Euler's rotation theorem, Euler's three-body problem and the Euler transform. Your Wikipedia article notes that mathematicians joke about a new rule: All new discoveries must be named after the second person who discovers them, to avoid naming them all after Euler. --F.R., Linguistics Moderator
Excellent, also starts with an 'e'. I got a chuckle out of the math joke, Fraggle. Predictably wry, lol....Please Register or Log in to view the hidden image!
What are you asking? No one really knows for sure why Euler chose the letter e as the symbol for this constant, which he tells us persuasively is one of the five most important numbers alongside 0, 1, π and i. Maybe it was because e stands for Euler. If you're asking why this number has the value it has, I would say that you're venturing into the realm of cosmology, where physics, philosophy and mathematics converge awkwardly. Why are the natural laws what they are, instead of something else? In most of the permutations, a universe could not exist that worked that way, so we wouldn't be here to ask the question. But for the few that might work, no one can say why we ended up with these instead of those. Maybe there's another universe somewhere that has those laws. You might as well ask why π has the value it has. One way to answer that question is that this value is the limit of the sum of the lengths of the sides of a regular polygon with a successively greater number of sides, used to approximate the circumference of a circle. I don't know as much about e as I do about π (which is: not very much really), so I can't give you such a clever reason for its value, but I'm sure a few minutes with Wikipedia or Google will deliver several of them to you. If neither of those questions is the one you're asking, then please ask again. This time use a whole lot more words, okay? Please Register or Log in to view the hidden image!
The definition of e has nothing to do with Cosmology, it is a purely mathematical definition. Specifically it is the number such that the derivative of \(y = e^x\) is equal to \(y\) ie \(\frac{d}{dx}e^x = e^x\). If you want a definition that doesn't directly involve calculus, e is sum of the infinite series \(e = \sum \limits_{n=0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \ldots\) where ! denotes a factorial: \(n! = n(n-1)(n-2) \ldots \times 2 \times 1\)
I like the natural growth definition: Consider something that grows at a rate that is always proportional to its current size: growth = size/T Where T is some constant amount of time. e is the factor by which the size increases in time T. For example, using kg, and setting T = 1 year... When the size is 1kg, the growth rate is 1kg/year When the size is 1.1kg, the growth rate is 1.1kg/year and so on. Exactly 1 year after the size is 1 kg, the size will be e kg Exactly 1 year after the size is 17kg, the size will be 17e kg and so on. I don't know if I wrote that awfully clearly.
Yes, I came to the thread thinking there was a discussion on why e is the transcendental number e. And yes it is in many ways like asking why is pi pi, both for natural reasons and mathematical reasons. I was curious if some of you sometimes ponder this, why elementary things are what they are. In a mathematical sense, it may take shape as a tedious question about something that needs no rigorous explanation, and the definition is most concisely stated as the function which is everywhere proportional to its derivative. From the natural sciences point of view, it may seem equally tedious to conceptualize it as anything more than the function that most generally describes growth and decay phenomena, where the instantaneous slope is inversely proportional to the time elapsed. And of course that is another way of saying the function is everywhere equal to its derivative. I was thinking not of the choice of symbol, or name, but the cause for this particular number to arise as a "magic number".
Why is a number a number (number can be e, π, 1, i or anything else) seems to be a meaningless question. After it is defined it is shown to have interesting properties, like e^πi = -1, but why doesn't enter into it.
