立方体の影の作図問題　解答(5)

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}0\\ 0\\ 0\end{array}\right)=\left(\begin{array}{c}0\\ 0\\ 0\end{array}\right)}$     ${\displaystyle {\text{A}}^{\prime }\left(0,0,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\sin 22.5°\\ \frac{1}{\sqrt{6}}+\frac{1}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{B}}^{\prime }\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}\sin 22.5°,\frac{\sqrt{6}}{6}+\frac{\sqrt{3}}{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}0\\ \sqrt{\frac{2}{3}}\\ \frac{2}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}-\frac{2}{\sqrt{3}}\sin 22.5°\\ \sqrt{\frac{2}{3}}+\frac{2}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{C}}^{\prime }\left(-\frac{2\sqrt{3}}{3}\sin 22.5°,\frac{\sqrt{6}}{3}+\frac{2\sqrt{3}}{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{6}}\\ \frac{1}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}-\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\sin 22.5°\\ \frac{1}{\sqrt{6}}+\frac{1}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{D}}^{\prime }\left(-\frac{\sqrt{2}}{2}-\frac{\sqrt{3}}{3}\sin 22.5°,\frac{\sqrt{6}}{6}+\frac{\sqrt{3}}{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}0\\ -\sqrt{\frac{2}{3}}\\ \frac{1}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}-\frac{1}{\sqrt{3}}\sin 22.5°\\ -\sqrt{\frac{2}{3}}+\frac{1}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{E}}^{\prime }\left(-\frac{\sqrt{3}}{3}\sin 22.5°,-\frac{\sqrt{6}}{3}+\frac{\sqrt{3}}{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}\frac{1}{\sqrt{2}}\\ -\frac{1}{\sqrt{6}}\\ \frac{2}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}\frac{1}{\sqrt{2}}-\frac{2}{\sqrt{3}}\sin 22.5°\\ -\frac{1}{\sqrt{6}}+\frac{2}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{F}}^{\prime }\left(\frac{\sqrt{2}}{2}-\frac{2\sqrt{3}}{3}\sin 22.5°,-\frac{\sqrt{6}}{6}+\frac{2\sqrt{3}}{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}0\\ 0\\ \sqrt{3}\end{array}\right)=\left(\begin{array}{c}-\sqrt{3}\sin 22.5°\\ \sqrt{3}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{G}}^{\prime }\left(-\sqrt{3}\sin 22.5°,\sqrt{3}\cos 22.5°,0\right)}$

${\displaystyle \left(\begin{array}{ccc}1& 0& -\sin 22.5°\\ 0& 1& \cos 22.5°\\ 0& 0& 0\end{array}\right)\left(\begin{array}{c}-\frac{1}{\sqrt{2}}\\ -\frac{1}{\sqrt{6}}\\ \frac{2}{\sqrt{3}}\end{array}\right)=\left(\begin{array}{c}-\frac{1}{\sqrt{2}}-\frac{2}{\sqrt{3}}\sin 22.5°\\ -\frac{1}{\sqrt{6}}+\frac{2}{\sqrt{3}}\cos 22.5°\\ 0\end{array}\right)}$     ${\displaystyle {\text{H}}^{\prime }\left(-\frac{\sqrt{2}}{2}-\frac{2\sqrt{3}}{3}\sin 22.5°,-\frac{\sqrt{6}}{6}+\frac{2\sqrt{3}}{3}\cos 22.5°,0\right)}$