diff options
Diffstat (limited to 'vorlesungen/slides/4/ggt.tex')
| -rw-r--r-- | vorlesungen/slides/4/ggt.tex | 43 |
1 files changed, 28 insertions, 15 deletions
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} |