From 6a56afa0e79fb4ac6f04c1d3c3a8e6314331989b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 16:04:13 +0100
Subject: new slides

---
 vorlesungen/slides/4/ggt.tex | 62 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 vorlesungen/slides/4/ggt.tex

(limited to 'vorlesungen/slides/4/ggt.tex')

diff --git a/vorlesungen/slides/4/ggt.tex b/vorlesungen/slides/4/ggt.tex
new file mode 100644
index 0000000..77b2a1d
--- /dev/null
+++ b/vorlesungen/slides/4/ggt.tex
@@ -0,0 +1,62 @@
+%
+% ggt.tex -- GGT, Definition und Algorithmus
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschuöe
+%
+\begin{frame}[t]
+\frametitle{Grösster gemeinsamer Teiler}
+\vspace{-15pt}
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Definition}
+Gegeben: $a,b\in\mathbb Z$
+\\
+Gesucht: grösster gemeinsamer Teiler $\operatorname{ggT}(a,b)$
+\end{block}
+\begin{block}{Euklidischer Algorithmus}
+$a_0 = a$, $b_0=b$
+\begin{align*}
+a_0&=b_0q_0 + r_0 & a_1 &=b_0 & b_1&=r_0 \\
+a_1&=b_1q_1 + r_1 & a_2 &=b_1 & b_2&=r_1 \\
+a_2&=b_2q_2 + r_2 & a_3 &=b_2 & b_3&=r_2 \\
+   &\;\vdots      &     &     &    &     \\
+a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&)=\operatorname{ggT}(a,b)
+\end{align*}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\begin{block}{$\operatorname{ggT}(15,25) = 5$}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.09]
+\draw[->] (-1,0) -- (65,0) coordinate[label={$a$}];
+\draw[->] (0,-1) -- (0,65) coordinate[label={right:$b$}];
+\begin{scope}
+\clip (-1,-1) rectangle (65,65);
+\foreach \x in {0,...,4}{
+	\draw[line width=0.2pt] ({\x*15},-2) -- ({\x*15},65);
+}
+\foreach \y in {0,...,2}{
+	\draw[line width=0.2pt] (-2,{\y*25}) -- (65,{\y*25});
+}
+\foreach \x in {0,5,...,120}{
+	\draw[color=blue] ({\x+2},-2) -- ({\x+2-70},{-2+70});
+	\node[color=blue] at ({0.5*\x-0.5},{0.5*\x-0.5}) [rotate=-45,above] {\tiny $\x$};
+}
+\foreach \x in {0,...,4}{
+	\foreach \y in {0,...,2}{
+		\fill[color=red] ({\x*15},{\y*25}) circle[radius=0.8];
+	}
+}
+\foreach \x in {0,5,...,60}{
+	\fill[color=blue] (\x,0) circle[radius=0.5];
+	\node at (\x,0) [below] {\tiny $\x$};
+}
+\end{scope}
+\end{tikzpicture}
+\end{center}
+\end{block}
+\end{column}
+\end{columns}
+\end{frame}
-- 
cgit v1.2.1


From ca12778acdf6f2da84aec311c5ab63cde5d847cd Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 1 Mar 2021 21:20:36 +0100
Subject: add slides

---
 vorlesungen/slides/4/ggt.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'vorlesungen/slides/4/ggt.tex')

diff --git a/vorlesungen/slides/4/ggt.tex b/vorlesungen/slides/4/ggt.tex
index 77b2a1d..e3c55e6 100644
--- a/vorlesungen/slides/4/ggt.tex
+++ b/vorlesungen/slides/4/ggt.tex
@@ -22,7 +22,7 @@ a_0&=b_0q_0 + r_0 & a_1 &=b_0 & b_1&=r_0 \\
 a_1&=b_1q_1 + r_1 & a_2 &=b_1 & b_2&=r_1 \\
 a_2&=b_2q_2 + r_2 & a_3 &=b_2 & b_3&=r_2 \\
    &\;\vdots      &     &     &    &     \\
-a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&)=\operatorname{ggT}(a,b)
+a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&=\operatorname{ggT}(a,b)
 \end{align*}
 \end{block}
 \end{column}
-- 
cgit v1.2.1


From f2454006fa4e2a0b4093507300fab8a29e3b5901 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 8 Mar 2021 09:40:32 +0100
Subject: final preparation

---
 vorlesungen/slides/4/ggt.tex | 43 ++++++++++++++++++++++++++++---------------
 1 file changed, 28 insertions(+), 15 deletions(-)

(limited to 'vorlesungen/slides/4/ggt.tex')

diff --git a/vorlesungen/slides/4/ggt.tex b/vorlesungen/slides/4/ggt.tex
index e3c55e6..ef97182 100644
--- a/vorlesungen/slides/4/ggt.tex
+++ b/vorlesungen/slides/4/ggt.tex
@@ -15,16 +15,22 @@ Gegeben: $a,b\in\mathbb Z$
 \\
 Gesucht: grösster gemeinsamer Teiler $\operatorname{ggT}(a,b)$
 \end{block}
+\uncover<4->{%
 \begin{block}{Euklidischer Algorithmus}
 $a_0 = a$, $b_0=b$
 \begin{align*}
-a_0&=b_0q_0 + r_0 & a_1 &=b_0 & b_1&=r_0 \\
-a_1&=b_1q_1 + r_1 & a_2 &=b_1 & b_2&=r_1 \\
-a_2&=b_2q_2 + r_2 & a_3 &=b_2 & b_3&=r_2 \\
-   &\;\vdots      &     &     &    &     \\
-a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&=\operatorname{ggT}(a,b)
+\uncover<5->{
+a_0&=b_0q_0 + r_0 & a_1 &=b_0 & b_1&=r_0}\\
+\uncover<6->{
+a_1&=b_1q_1 + r_1 & a_2 &=b_1 & b_2&=r_1}\\
+\uncover<7->{
+a_2&=b_2q_2 + r_2 & a_3 &=b_2 & b_3&=r_2}\\
+\uncover<8->{
+   &\;\vdots      &     &     &    &    }\\
+\uncover<9->{
+a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&=\operatorname{ggT}(a,b)}
 \end{align*}
-\end{block}
+\end{block}}
 \end{column}
 \begin{column}{0.48\textwidth}
 \begin{block}{$\operatorname{ggT}(15,25) = 5$}
@@ -40,18 +46,25 @@ a_n&=b_nq_n + r_n & r_n &= 0  & r_{n-1}&=\operatorname{ggT}(a,b)
 \foreach \y in {0,...,2}{
 	\draw[line width=0.2pt] (-2,{\y*25}) -- (65,{\y*25});
 }
-\foreach \x in {0,5,...,120}{
-	\draw[color=blue] ({\x+2},-2) -- ({\x+2-70},{-2+70});
-	\node[color=blue] at ({0.5*\x-0.5},{0.5*\x-0.5}) [rotate=-45,above] {\tiny $\x$};
+\uncover<3->{
+	\foreach \x in {0,5,...,120}{
+		\draw[color=blue] ({\x+2},-2) -- ({\x+2-70},{-2+70});
+		\node[color=blue] at ({0.5*\x-0.5},{0.5*\x-0.5})
+			[rotate=-45,above] {\tiny $\x$};
+	}
 }
-\foreach \x in {0,...,4}{
-	\foreach \y in {0,...,2}{
-		\fill[color=red] ({\x*15},{\y*25}) circle[radius=0.8];
+\uncover<2->{
+	\foreach \x in {0,...,4}{
+		\foreach \y in {0,...,2}{
+			\fill[color=red] ({\x*15},{\y*25}) circle[radius=0.8];
+		}
 	}
 }
-\foreach \x in {0,5,...,60}{
-	\fill[color=blue] (\x,0) circle[radius=0.5];
-	\node at (\x,0) [below] {\tiny $\x$};
+\uncover<3->{
+	\foreach \x in {0,5,...,60}{
+		\fill[color=blue] (\x,0) circle[radius=0.5];
+		\node at (\x,0) [below] {\tiny $\x$};
+	}
 }
 \end{scope}
 \end{tikzpicture}
-- 
cgit v1.2.1

