Professor @TedShifrin, on the question of differential geometry, I can not seem to help that person out. What am I doing wrong?
I am assuming that all derivatives of $\alpha$ are with respect to $t$. Now there is an identity we can use:
$$|a\times b|^{2} = |a|^{2}|b|^{2}-(a\cdot b)^{2}.$$
Therefore,
$$\begin{align}
|\alpha'\times \alpha''|^2 &= |\alpha'|^{2}|\alpha''|^{2}-(\alpha'\cdot \alpha'')^{2}\\
& = |\alpha'|^{2}|\alpha''|^{2},\\
\end{align}
$$
since $\alpha'$ and $\alpha''$ are orthogonal. Therefore we have that
How can one get $2015$ using $1,2,\dots,9$ in this order and only once, with the operations $+,-,\times,/$ ?
Solving this riddle with a computer (using python) turned out to be impossible for me due to the amount of memory needed.
Hence, I am looking for a mathematical way to find the/a sol...
