diff options
author | LordMcFungus <mceagle117@gmail.com> | 2021-03-22 18:05:11 +0100 |
---|---|---|
committer | GitHub <noreply@github.com> | 2021-03-22 18:05:11 +0100 |
commit | 76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7 (patch) | |
tree | 11b2d41955ee4bfa0ae5873307c143f6b4d55d26 /vorlesungen/slides/4/ggt.tex | |
parent | more chapter structure (diff) | |
parent | add title image (diff) | |
download | SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.tar.gz SeminarMatrizen-76d2d77ddb2bed6b7c6b8ec56648d85da4103ab7.zip |
Merge pull request #1 from AndreasFMueller/master
update
Diffstat (limited to '')
-rw-r--r-- | vorlesungen/slides/4/ggt.tex | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/vorlesungen/slides/4/ggt.tex b/vorlesungen/slides/4/ggt.tex new file mode 100644 index 0000000..ef97182 --- /dev/null +++ b/vorlesungen/slides/4/ggt.tex @@ -0,0 +1,75 @@ +% +% 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} +\uncover<4->{% +\begin{block}{Euklidischer Algorithmus} +$a_0 = a$, $b_0=b$ +\begin{align*} +\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{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}); +} +\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 $\x$}; + } +} +\uncover<2->{ + \foreach \x in {0,...,4}{ + \foreach \y in {0,...,2}{ + \fill[color=red] ({\x*15},{\y*25}) circle[radius=0.8]; + } + } +} +\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} +\end{center} +\end{block} +\end{column} +\end{columns} +\end{frame} |