2,739 reputation
2336
bio website ephorie.de
location Germany
age 44
visits member for 4 years, 6 months
seen 4 hours ago

just an amateur fascinated by math


Aug
8
answered What do $\pi$ and $e$ stand for in the normal distribution formula?
Aug
7
comment What do $\pi$ and $e$ stand for in the normal distribution formula?
The plots from my answer would have come in handy ;-)
Aug
7
comment What do $\pi$ and $e$ stand for in the normal distribution formula?
A further indication that there is no special connection between the two constants via this formula is when you use the general base $a$ but don't square the exponents: Integration won't give you $\pi$ because it is not rotationally symmetric any more (just plot it) - but $e$ still crops up (via the natural log) due to the integration operation.
Aug
7
comment What do $\pi$ and $e$ stand for in the normal distribution formula?
Yes, this division by the logarithm is due to the horizontal rescaling I mentioned above. That a logarithm shows up is just a consequence of "bringing down" the exponent. The natural logarithm is a convenient closed form. But it is true: $e$ keeps showing up - I have to think about that but at the moment I think that is because of its deep connection to differentiation/integration in general, and that is what we are doing here after all. So I don't think that this special curve really connects $\pi$ and $e$. But always interesting to think about these basic ideas that are so fundamental!
Aug
7
comment What do $\pi$ and $e$ stand for in the normal distribution formula?
@George: I don't think that Euler's identity is of any help here. See also my answer below.
Aug
7
answered What do $\pi$ and $e$ stand for in the normal distribution formula?
Jul
29
awarded  Yearling
Jul
21
accepted Proof that the first reappearing remainder when dividing one by a prime number is one
Jul
21
comment Proof that the first reappearing remainder when dividing one by a prime number is one
Thank you! Is it perhaps possible to proof that the first reappearing remainder when dividing one by a prime number is one directly follows from the condition that if the expansion of $1/p$ recurs with period $k$ then $10^k−1$ is divisible by $p$? I don't see that this is a direct consequence of your answer.
Jul
21
revised Proof that the first reappearing remainder when dividing one by a prime number is one
added 256 characters in body
Jul
21
revised Proof that the first reappearing remainder when dividing one by a prime number is one
edited tags
Jul
21
asked Proof that the first reappearing remainder when dividing one by a prime number is one
Jul
15
accepted Which internal angles can a lattice polygon have?
Jul
15
comment Which internal angles can a lattice polygon have?
@Qiaochu: This is an interesting comment. I haven't thought about that (and I am not sure if it will help me) but it is fascinating nonetheless. Thank you.
Jul
15
asked Which internal angles can a lattice polygon have?
Jun
30
answered The intuition behind generalized eigenvectors
Jun
28
answered Quick inverse trigonometric integration question.
Jun
28
answered Learning mathematics as if an absolute beginner?
Jun
27
accepted Proof for law of complex exponents using only differential equation
Jun
27
comment Proof for law of complex exponents using only differential equation
Now I see, very elegant proof - Thank you again!