In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point. A choice of surface normal allows one to use the right-hand rule to define a "clockwise" direction of loops in the surface, as needed by Stokes' theorem for instance. More generally, orientability of an abstract surface, or manifold, measures whether one can consistently choose a "clockwise" orientation for all loops in the manifold. Equivalently, a surface is orientable if a two-dimensional figure such as in the space...
Look at this sequence:
2,2,2,2,2,3,3,2,2,2,2,2,3,3,2,2,2,2,2,3,3...
It is defined as fallow:
$$f(n)=\begin{cases}
3 &\text{if $n \bmod 7=6,0$}\\
2 &\text{otherwise}\\
\end{cases}$$
David found a good representation for $f(n)$:
$$g(n)=\frac{\sin\dfrac{2\pi(n+1)}{7}}{\sin\dfrac{2\pi}{7}}
...
$$P(x, y)=0 \tag {1} \\ \text{ where }P(x, y) \in \mathbb{Q}[x, y]$$
How do we know that $(1)$ has a solution in a $\mathbb{Q}_p$ ?
We will apply Hensel's Lemma.
Idea: we begin from an element of $\mathbb{Q}_p$, that has some identities $(a_1)$.
Then we create a sequence of values $a_1, ...
