Timeline for The "e" in apple
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| yesterday | comment | added | Dan | @Pranay I suppose there might not be such motivation (other than to solve this math puzzle), and that's probably why the fact that e is found in a ball is rarely mentioned. You might say that e is "hidden" in a ball. | |
| yesterday | vote | accept | Dan | ||
| yesterday | comment | added | Pranay | @Dan. As I said at the end of my answer, I was trying to see if this limit is an answer to a geometric or probabilistic question. Without such motivation, just writing this expression seems a bit vague to me. | |
| yesterday | comment | added | Dan | @Pranay By the way, I wonder why you felt this solution was vague? If we think about it like $\lim\limits_{r/R\to 0}\left(\frac{r}{y}\right)^\frac{R}{Y}=e$, it is clear (to me at least) that this shows that $e$ is found in a ball. | |
| yesterday | comment | added | Dan | @Pranay Yes, y and Y are equal. I give it two names, for a purely aesthetic reason: the limit expression is conceptually more symmetrical. | |
| yesterday | comment | added | Pranay | @Lucenaposition. See my response to Dan's comment above. | |
| yesterday | comment | added | Pranay | @Dan. In your notation, what I mean is $\lim_{r/R \to 0} (r/y)^{(R+r)/r} = e$. But yours works as well because $R/r \approx R/y$ in the limit and $y=Y$. (I don't know why you have to define $y$ and $Y$ separately since they are the same.) | |
| yesterday | comment | added | Pranay | @FirstNameLastName. I was wondering the same thing, but couldn't make it work. | |
| yesterday | comment | added | Lucenaposition | What about $(y/r)^{-R/Y}$ which is equal? | |
| yesterday | comment | added | Dan | @Pranay Is this what you mean: $\lim\limits_{r/R\to 0}\left(\frac{r}{y}\right)^\frac{R}{Y}=e$ | |
| yesterday | comment | added | FirstName LastName | I had an idea of systematically, perhaps using powers, covering bigger area with smaller ones, perhaps leaving gaps to eventually be ignored, but I can't get the proportions and ratios correct. | |
| yesterday | history | answered | Pranay | CC BY-SA 4.0 |