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If $x=f(a)$ is solved for $a\in\mathbb Q$ and $f(a)$ is continuous, then $x=f(a)$ for $a\notin\mathbb Q$.
Next, we see that if $a\ne0,a\in\mathbb Q$, then $x$ is not algebraic. If $x$ were algebraic, then $\sin(x)$ would be transcendental, and thus $x\sin(x)$ would be transcendental, a contradi...
Here are three more gems presented in chronological order.
Viète and the first infinite product in the history of mathematics (1593)
\begin{align*}
\frac{2}{\pi}=\sqrt{\frac{1}{2}}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}}
\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}...
This is somewhat of a follow-up to a previous question which asked in a roundabout way about how to walk upon a parametric surface approximated by triangular faces. Now I want to know is whether or not my proposed construction of the model itself will actually work in the way I imagine.
Suppos...
