MathJax
Posted: Wed Aug 31, 2016 11:31 am
MathJax is great!
\(\text{Lattice} = \begin{matrix}
&& \Bbb Q(\sqrt{2},i) & \\
&\huge\diagup & \huge| & \huge\diagdown \\
\Bbb Q(\sqrt{2}) & & \Bbb Q(i\sqrt{2})& & \Bbb Q(i)\\
&\huge\diagdown & \huge| & \huge\diagup \\
&&\Bbb Q
\end{matrix}\)
Again,
\( \begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
& = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
& = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
& = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
& \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}\)
\(\text{Lattice} = \begin{matrix}
&& \Bbb Q(\sqrt{2},i) & \\
&\huge\diagup & \huge| & \huge\diagdown \\
\Bbb Q(\sqrt{2}) & & \Bbb Q(i\sqrt{2})& & \Bbb Q(i)\\
&\huge\diagdown & \huge| & \huge\diagup \\
&&\Bbb Q
\end{matrix}\)
Again,
\( \begin{align}
\sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
& = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\
& = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
& = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\
& \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
\end{align}\)