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many improvements (theorem-proof-structure for constant function; corrected errors)

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Martin Thoma 2013-12-21 19:10:35 +01:00
parent 01e343f66c
commit a1274e176f
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documents/math-minimal-distance-to-cubic-function/quadratic-case-2.3.tex
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@ -10,8 +10,7 @@
&= 12 \cdot \bigg (\frac{\overbrace{\sqrt[3]{12} \alpha (1-i \sqrt{3}) - t^2(1+i\sqrt{3})}^{\text{numerator}}}{12t} \bigg )^3
\end{align}
Now calculate the numerator$^3$. Remember, that $(1-i \sqrt{3})^2 = -2 (1+i \sqrt{3})$
and $(1 \pm i \sqrt{3})^3 = -8$.
Now calculate the numerator$^3$:
\begin{align}
\left (\sqrt[3]{12} \alpha (1-i \sqrt{3}) - t^2(1+i\sqrt{3}) \right )^3 &=
12 \alpha^3 (1-i\sqrt{3})^3 \\