Linked Questions

6
votes
7answers
2k views

How would you explain why “e” is important? (And when it applies?) [duplicate]

Possible Duplicate: Intuitive Understanding of the constant ā€œeā€ Let's say you want to explain this to your teenage son. I understand the technical definition of $e$ $$ ...
2
votes
5answers
320 views

Can someone please explain $e$ in layman's term? [duplicate]

I never really understood what $e$ means and I'm always terrified when I see it in equations. What is it? Can somebody dumb it down for me? I know it's a constant. Is it as simple as that?
0
votes
4answers
116 views

what is $e$ really? what is its meaning? [duplicate]

I don't get it how we came up with $e$ and how can nature use this number so much! that is what I have been told and I only know that $e$ is a specific constant like $\pi$! I understand that $\pi$ ...
2
votes
5answers
176 views

What's so special about $e$? [duplicate]

If someone with not much mathematics in his luggage asks me: What is so special about $\pi$? then off course I have an answer. Even if $i$ would be the subject (I allready see him gazing at my ...
2
votes
0answers
215 views

What is the constant $e$, fundamentally? [duplicate]

Possible Duplicate: Why is the number e so important in mathematics? Intuitive Understanding of the constant “e” The number $e$ is important in many respects. If you ask ...
1
vote
1answer
87 views

Practical significance of $e$ [duplicate]

We know, for example, the constant $\pi$ is the perimeter of a circle with diameter $1$ unit. In the similar manner how would we explain the constant $e$. I have searched a lot for it. But I couldn't ...
37
votes
20answers
8k views

Proof that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$?

I am just starting into calculus and I have a question about the following statement I encountered while learning about definite integrals: $$\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$$ I really ...
49
votes
9answers
18k views

Why is Pi equal to 3.14159…?

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any ...
28
votes
20answers
3k views

Could you explain why $\frac{d}{dx} e^x = e^x$ “intuitively”?

As the title implies, It is seems that $e^x$ is the only function whoes derivative is the same as itself. thanks.
11
votes
5answers
2k views

Why is it trivial that $\left(1+\frac{2\ln3}{3}\right)^{-3/2}\leq\frac{2}{3}$?

Can someone tell me why $$\left(1+\dfrac{2\ln3}{3}\right)^{-3/2}\leq\dfrac{2}{3}$$ is trivial because for me its not and I will need to do the calculation to see it.
13
votes
6answers
430 views

$\pi$ from the unit circle, $\sqrt 2$ from the unit square but what about $e$? [duplicate]

If one wants to introduce $\pi$ to a not mathematically savvy person, the unit circle would be a good choice. The unit square would be the way to go for $\sqrt 2$. But what about $e$? I've reviewed ...
6
votes
2answers
509 views

Two questions about Euler's number $e$

I am on derivatives at the moment and I just bumped into this number $e$, "Euler's number" . I am told that this number is special especially when I take the derivative of $e^x$ , because its slope of ...
3
votes
2answers
144 views

What is the speciality of 'e' in mathematics?

If we have to find differential coefficient of $x$ to the power $x$ with respect to $x$ , we take logarithm base $e$ of both sides of $x^x=y$. Why is $e$ selected as base instead of any other number ? ...

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