[tag:tagname]
syntax is not rendered in your previous message: chat.stackexchange.com/transcript/message/52799505#52799505 @username
. Alexander Gruber probably wasn't in this room for some time - so he isn't pingable in this way. But using direct reply to one of this older messages (as I did above) should give him notification. 
The coefficient of similarity between two circles $C$ and $C’$ of radii $r$ and $r’$ is $$\frac{r}{r’}=\frac {k}{k_n},$$ where $k$ is the radius of inversion and $k_n$ is the square of the length of a tangent to $C’$.
Why is this the case? I spent a lot of time trying to show it geometricall...

Typically, Wilson's is given as
$$(n-1)! \equiv -1 \pmod{n},$$
which is short and sweet, but I came up with an alternate presentation of it that's arguably needlessly complicated, but also arguably illustrative:
$$\prod_{i=1}^{n}i \equiv \sum_{i=1}^{n}{1} \pmod{\sum_{i=1}^{n}{i}}.$$
This show...

According to the Scholarpedia defintion:
a function $F$ of real variable $t$ such that $F(t) = f(\omega_1t,\cdots, \omega_m t)$
for some continuous function $f(\phi_1,\cdots,\phi_m)$
of $m$ variables $(m≥2)$, periodic on $\phi_1,\cdots,\phi_m$ with the period $2\pi$, and some set of posi...

Recently, I was investigating the following equation:
$$p\pi = qe, p,q \in \Bbb{N}$$
I then plot the sets $\{p\pi\}$ in black,$\{qe\}$ in yellow and obtained the following plot:
which apparently it has some kind of fringes that looks evenly spaced, suggesting some kind of periodicity.
To inves...

Has anyone produced a quasiperiodic tiling of the hyperbolic plane?
Or is there a reason it cannot be done?
By quasiperiodic I mean that the structure is not strictly periodic (i.e. equal to itsef after translation) but that any arbitrary large neighbourhood of any point can be found identicall...

Sums of trigonometric functions may or may not be periodic functions; in particular, $\sin(ax)+\sin(bx)$ is periodic if $a/b$ is rational.
If we consider the function
\begin{equation}
f(x) = \sin(3x) + \sin(\pi x)
\end{equation}
it surely looks periodic, even if it's not; to me it feels like the...

Define $$f(x)=\frac{\cos^2(\pi x)}{2+\cos(x)}$$
We know that $f(x)$ is not periodic. Is there any way to write $f(x)$ as the sum of two periodic functions. That is, find periodic functions $f_1(x)$ and $f_2(x)$ such that $f(x)=f_1(x)+f_2(x)$.

I am doing some work regarding quasiperiodic functions but I am not able to figure out the difference between almost periodic and quasiperiodic functions. Can anyone let me know about it?

I posted a question in such a garbled form that I thought I should repost separately. I have deleted the other post just to remove it from consideration. Apologies for that.
I am playing with a complicated quasi-periodic equation, $f(x)$, which boils down to a summation of sines and cosines. I c...
{0-forms on U} -> {1-forms on U} -> {2-forms on U} -> {3 forms on U}
Using the usual inner product (and orientation) on R^3 lets us regard this as a sequence of maps
« first day (2732 days earlier) ← previous day next day → last day (1900 days later) »