From 15881729aa3f1293d546a1692a02094ed3f24e2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sun, 11 Apr 2021 10:30:05 +0200
Subject: phases

---
 vorlesungen/slides/7/drehung.tex | 53 +++++++++++++++++++++++++++-------------
 1 file changed, 36 insertions(+), 17 deletions(-)

(limited to 'vorlesungen/slides/7/drehung.tex')

diff --git a/vorlesungen/slides/7/drehung.tex b/vorlesungen/slides/7/drehung.tex
index ae0dbe3..7744e99 100644
--- a/vorlesungen/slides/7/drehung.tex
+++ b/vorlesungen/slides/7/drehung.tex
@@ -13,12 +13,20 @@
 \begin{columns}[t,onlytextwidth]
 \begin{column}{0.38\textwidth}
 \begin{block}{Drehung}
+{\color{blue}Längen}, {\color<2->{blue}Winkel},
+{\color<2->{darkgreen}Orientierung}
+erhalten
+\uncover<2->{
 \[
 \operatorname{SO}(2)
 =
-\operatorname{SL}_2(\mathbb{R}) \cap \operatorname{O}(2)
-\]
+{\color{blue}\operatorname{O}(2)}
+\cap
+{\color{darkgreen}\operatorname{SL}_2(\mathbb{R})}
+\]}
+\vspace{-20pt}
 \end{block}
+\uncover<3->{%
 \begin{block}{Zusammensetzung}
 Eine Drehung muss als Zusammensetzung geschrieben werden können:
 \[
@@ -31,7 +39,9 @@ D_{\alpha}
 =
 DST
 \]
-\end{block}
+\end{block}}
+\vspace{-10pt}
+\uncover<12->{%
 \begin{block}{Beispiel}
 \vspace{-12pt}
 \[
@@ -43,9 +53,10 @@ D_{60^\circ}
 \begin{pmatrix}1&0\\\frac{\sqrt{3}}2&1\end{pmatrix}
 }
 \]
-\end{block}
+\end{block}}
 \end{column}
 \begin{column}{0.58\textwidth}
+\uncover<4->{%
 \begin{block}{Ansatz}
 \vspace{-12pt}
 \begin{align*}
@@ -64,7 +75,7 @@ c^{-1}&0\\
 t&1
 \end{pmatrix}
 \\
-&=
+&\uncover<5->{=
 \begin{pmatrix}
 c^{-1}&0\\
   0   &c
@@ -73,40 +84,48 @@ c^{-1}&0\\
 -st&-s\\
   t& 1
 \end{pmatrix}
+}
 \\
-&=
+&\uncover<6->{=
 \begin{pmatrix}
--stc^{-1}&{\color{darkgreen}sc^{-1}}\\
-{\color{blue}ct}&{\color{red}c}
-\end{pmatrix}
-=
+{\color<11->{orange}-stc^{-1}}&{\color<10->{darkgreen}sc^{-1}}\\
+{\color<9->{blue}ct}&{\color<8->{red}c}
+\end{pmatrix}}
+\uncover<7->{=
 \begin{pmatrix}
-\cos\alpha & {\color{darkgreen}- \sin\alpha} \\
-{\color{blue}\sin\alpha} & \phantom{-}  {\color{red}\cos\alpha}
-\end{pmatrix}
+{\color<11->{orange}\cos\alpha} & {\color<10->{darkgreen}- \sin\alpha} \\
+{\color<9->{blue}\sin\alpha} & \phantom{-}  {\color<8->{red}\cos\alpha}
+\end{pmatrix}}
 \end{align*}
-\end{block}
+\end{block}}
 \vspace{-10pt}
+\uncover<7->{%
 \begin{block}{Koeffizientenvergleich}
 \vspace{-15pt}
 \begin{align*}
+\uncover<8->{
 {\color{red} c}
 &=
-{\color{red}\cos\alpha }
+{\color{red}\cos\alpha }}
 &&
 &
+\uncover<9->{
 {\color{blue}
-t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$} \\
+t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$}}\\
+\uncover<10->{
 {\color{darkgreen}sc^{-1}}&={\color{darkgreen}-\sin\alpha}
 &
 &\Rightarrow&
 {\color{darkgreen}s}&={\color{darkgreen}-\sin\alpha}\cos\alpha
+}
 \\
+\uncover<11->{
 {\color{orange} -stc^{-t}}
 &=
 \rlap{$\sin\alpha\tan\alpha = \cos\alpha \quad $}
+}
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \end{columns}
 \end{frame}
-- 
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