In the comments under my proposal in the tag management thread, @AlexanderGruber has suggested (in my view) a better way to resolve the issues with tagging questions about the gradient, namely, creating a [tag:grad-curl-div] tag that would subsume the intended scope of the [tag:gradient] tag and (presumably) would have [tag:gradient], [tag:curl], and [tag:divergence] tags as synonyms. My edit includes proposed a tag-excerpt and tag-wiki, and lists some advantages of implementing this proposal:
Proposal: Add the tag grad-curl-div; make gradient, curl and div aliases thereof.
Edit 2: I've revised the proposal statement to Alexander Gruber's (in my view superior) suggestion in the comments. Implementing this proposal poses some advantages over the status quo:
It would (productively) fr...
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In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied.
The concept of inversion can be generalized to higher-dimensional spaces.
== Circle inversion ==
=== Inverse of a point... ===
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In number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n. That is (using the notations of modular arithmetic), the factorial
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{\displaystyle (n-1)!=1\times 2\times 3\times \cdots \times (n-1)}
satisfies
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Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an almost periodic function, which has increasing regularity over multiple periods. The mathematical definition of quasiperiodic function is a completely different concept; the two should not be confused.
== Climatology ==
In climatol...
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Q: What give rise to the apparent quasiperiodicity of integer multiples of $\pi$ and $e$ plotted here?
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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...
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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...
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Resolved (mostly) Creation of a tag gcd-and-lcm. Merge of the GCD part, not yet merged the LCM part, in case some objection emerges. The tag wiki might need some (more) attention.
Proposal: merge gcd and lcm
We tend to combine homologus objects into one tag, like supremum-and-infimum, limsup...
