From 1fb743df08b0734932d510c6b11405d0a2dbbe47 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Sat, 10 Apr 2021 19:57:13 +0200
Subject: new slides

---
 vorlesungen/slides/7/drehung.tex | 113 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 113 insertions(+)
 create mode 100644 vorlesungen/slides/7/drehung.tex

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

diff --git a/vorlesungen/slides/7/drehung.tex b/vorlesungen/slides/7/drehung.tex
new file mode 100644
index 0000000..ae0dbe3
--- /dev/null
+++ b/vorlesungen/slides/7/drehung.tex
@@ -0,0 +1,113 @@
+%
+% drehung.tex -- Drehung aus streckungen
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Drehung aus Streckungen und Scherungen}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.38\textwidth}
+\begin{block}{Drehung}
+\[
+\operatorname{SO}(2)
+=
+\operatorname{SL}_2(\mathbb{R}) \cap \operatorname{O}(2)
+\]
+\end{block}
+\begin{block}{Zusammensetzung}
+Eine Drehung muss als Zusammensetzung geschrieben werden können:
+\[
+D_{\alpha} 
+=
+\begin{pmatrix}
+\cos\alpha & -\sin\alpha\\
+\sin\alpha &\phantom{-}\cos\alpha
+\end{pmatrix}
+=
+DST
+\]
+\end{block}
+\begin{block}{Beispiel}
+\vspace{-12pt}
+\[
+D_{60^\circ}
+=
+{\tiny
+\begin{pmatrix}2&0\\0&\frac12\end{pmatrix}
+\begin{pmatrix}1&-\frac{\sqrt{3}}4\\0&1\end{pmatrix}
+\begin{pmatrix}1&0\\\frac{\sqrt{3}}2&1\end{pmatrix}
+}
+\]
+\end{block}
+\end{column}
+\begin{column}{0.58\textwidth}
+\begin{block}{Ansatz}
+\vspace{-12pt}
+\begin{align*}
+DST
+&=
+\begin{pmatrix}
+c^{-1}&0\\
+  0   &c
+\end{pmatrix}
+\begin{pmatrix}
+1&-s\\
+0&1
+\end{pmatrix}
+\begin{pmatrix}
+1&0\\
+t&1
+\end{pmatrix}
+\\
+&=
+\begin{pmatrix}
+c^{-1}&0\\
+  0   &c
+\end{pmatrix}
+\begin{pmatrix}
+-st&-s\\
+  t& 1
+\end{pmatrix}
+\\
+&=
+\begin{pmatrix}
+-stc^{-1}&{\color{darkgreen}sc^{-1}}\\
+{\color{blue}ct}&{\color{red}c}
+\end{pmatrix}
+=
+\begin{pmatrix}
+\cos\alpha & {\color{darkgreen}- \sin\alpha} \\
+{\color{blue}\sin\alpha} & \phantom{-}  {\color{red}\cos\alpha}
+\end{pmatrix}
+\end{align*}
+\end{block}
+\vspace{-10pt}
+\begin{block}{Koeffizientenvergleich}
+\vspace{-15pt}
+\begin{align*}
+{\color{red} c}
+&=
+{\color{red}\cos\alpha }
+&&
+&
+{\color{blue}
+t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$} \\
+{\color{darkgreen}sc^{-1}}&={\color{darkgreen}-\sin\alpha}
+&
+&\Rightarrow&
+{\color{darkgreen}s}&={\color{darkgreen}-\sin\alpha}\cos\alpha
+\\
+{\color{orange} -stc^{-t}}
+&=
+\rlap{$\sin\alpha\tan\alpha = \cos\alpha \quad $}
+\end{align*}
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


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}
-- 
cgit v1.2.1


From eb8f7d58101bd19006019dfbfafca92dd080fe41 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 12 Apr 2021 13:30:14 +0200
Subject: typos, new slides

---
 vorlesungen/slides/7/drehung.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

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

diff --git a/vorlesungen/slides/7/drehung.tex b/vorlesungen/slides/7/drehung.tex
index 7744e99..2d7b317 100644
--- a/vorlesungen/slides/7/drehung.tex
+++ b/vorlesungen/slides/7/drehung.tex
@@ -50,7 +50,7 @@ D_{60^\circ}
 {\tiny
 \begin{pmatrix}2&0\\0&\frac12\end{pmatrix}
 \begin{pmatrix}1&-\frac{\sqrt{3}}4\\0&1\end{pmatrix}
-\begin{pmatrix}1&0\\\frac{\sqrt{3}}2&1\end{pmatrix}
+\begin{pmatrix}1&0\\\sqrt{3}&1\end{pmatrix}
 }
 \]
 \end{block}}
@@ -81,14 +81,14 @@ c^{-1}&0\\
   0   &c
 \end{pmatrix}
 \begin{pmatrix}
--st&-s\\
-  t& 1
+1-st&-s\\
+   t& 1
 \end{pmatrix}
 }
 \\
 &\uncover<6->{=
 \begin{pmatrix}
-{\color<11->{orange}-stc^{-1}}&{\color<10->{darkgreen}sc^{-1}}\\
+{\color<11->{orange}(1-st)c^{-1}}&{\color<10->{darkgreen}sc^{-1}}\\
 {\color<9->{blue}ct}&{\color<8->{red}c}
 \end{pmatrix}}
 \uncover<7->{=
@@ -120,9 +120,9 @@ t}&=\rlap{$\displaystyle\frac{\sin\alpha}{c} = \tan\alpha$}}\\
 }
 \\
 \uncover<11->{
-{\color{orange} -stc^{-t}}
+{\color{orange} (1-st)c^{-t}}
 &=
-\rlap{$\sin\alpha\tan\alpha = \cos\alpha \quad $}
+\rlap{$\displaystyle\frac{(1-\sin^2\alpha)}{\cos\alpha} = \cos\alpha $}
 }
 \end{align*}
 \end{block}}
-- 
cgit v1.2.1


From 3fe0e1a234175903de4a161444b9db9810956f9d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 29 Apr 2021 09:03:37 +0200
Subject: add new slides

---
 vorlesungen/slides/7/drehung.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

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

diff --git a/vorlesungen/slides/7/drehung.tex b/vorlesungen/slides/7/drehung.tex
index 2d7b317..02201d4 100644
--- a/vorlesungen/slides/7/drehung.tex
+++ b/vorlesungen/slides/7/drehung.tex
@@ -58,7 +58,7 @@ D_{60^\circ}
 \begin{column}{0.58\textwidth}
 \uncover<4->{%
 \begin{block}{Ansatz}
-\vspace{-12pt}
+%\vspace{-12pt}
 \begin{align*}
 DST
 &=
@@ -101,7 +101,7 @@ c^{-1}&0\\
 \vspace{-10pt}
 \uncover<7->{%
 \begin{block}{Koeffizientenvergleich}
-\vspace{-15pt}
+%\vspace{-15pt}
 \begin{align*}
 \uncover<8->{
 {\color{red} c}
-- 
cgit v1.2.1

