Anonymous
The helicity of a smooth vector field defined on a domain in 3D space is the standard measure of the extent to which the field lines wrap and coil around one another. As to magnetic helicity, this "vector field" is magnetic field. It is a generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. As with many quantities in electromagnetism, magnetic helicity (which describes magnetic field lines) is closely related to fluid mechanical helicity (which describes fluid flow lines).
If magnetic field lines follow the strands of...
3
Let us try to understand $\lambda$ first. Suppose in general that $L, L'$ are two linked (but disjoint) circles in $\Bbb R^3$ and you look at the map $\lambda : L \times L' \to S^2$ defined analogously. Then $\lambda(\mathbf{x}, \mathbf{y})$ is truly the unit direction vector from $\mathbf{x}$ to...
The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula.
In polar coordinates, with
r
{\displaystyle r}
the radius and
φ
{\displaystyle \varphi }
the angle, the superformula is:
r
(
φ
...
In mathematics, sexy primes are prime numbers that differ from each other by six. For example, the numbers 5 and 11 are both sexy primes, because 11 minus 5 is 6. If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime triplet.
The term "sexy prime" stems from the Latin word for six: sex.
== n# notation ==
As used in this article, n# stands for the product 2 · 3 · 5 · 7 · … of all the primes ≤ n.
== Types of groupings ==
=== Sexy prime pairs ===
The sexy primes (sequences A023201 and A046117 in OEIS) below 500 are:
(5,11), (7,13), (11,17...
