From 1cc2af1d5f61c848cb1fcccdc021addfb0e1626e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Tue, 18 May 2021 20:24:21 +0200
Subject: add new slides

---
 vorlesungen/slides/9/pf/dreieck.tex | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)
 create mode 100644 vorlesungen/slides/9/pf/dreieck.tex

(limited to 'vorlesungen/slides/9/pf/dreieck.tex')

diff --git a/vorlesungen/slides/9/pf/dreieck.tex b/vorlesungen/slides/9/pf/dreieck.tex
new file mode 100644
index 0000000..ba26e9e
--- /dev/null
+++ b/vorlesungen/slides/9/pf/dreieck.tex
@@ -0,0 +1,19 @@
+%
+% dreieck.tex -- slide template
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Verallgemeinerte Dreiecksungleichung}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\end{column}
+\begin{column}{0.48\textwidth}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
cgit v1.2.1


From cd89b4b8b98a5ac8bfc3f4182df01b1b80f33c79 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Wed, 19 May 2021 20:42:21 +0200
Subject: new slides

---
 vorlesungen/slides/9/pf/dreieck.tex | 29 +++++++++++++++++++++++++++--
 1 file changed, 27 insertions(+), 2 deletions(-)

(limited to 'vorlesungen/slides/9/pf/dreieck.tex')

diff --git a/vorlesungen/slides/9/pf/dreieck.tex b/vorlesungen/slides/9/pf/dreieck.tex
index ba26e9e..0a572f3 100644
--- a/vorlesungen/slides/9/pf/dreieck.tex
+++ b/vorlesungen/slides/9/pf/dreieck.tex
@@ -10,9 +10,34 @@
 \frametitle{Verallgemeinerte Dreiecksungleichung}
 \vspace{-20pt}
 \begin{columns}[t,onlytextwidth]
-\begin{column}{0.48\textwidth}
+\begin{column}{0.32\textwidth}
+\begin{block}{Satz}
+\[
+|u+v|\le |u|+|v|
+\]
+Gleichheit wenn lin.~abh.
+\end{block}
+\begin{block}{Satz}
+\[
+\biggl|\sum_i u_i\biggr|
+\le
+\sum_i |u_i|
+\]
+Gleichheit wenn $u_i = \lambda_i u$
+\end{block}
+\begin{block}{Satz}
+\[
+\biggl|\sum_i z_i\biggr|
+\le
+\sum_i |z_i|
+\]
+Gleichheit, wenn $z_i=|z_i|c$, $c\in\mathbb{C}$
+\end{block}
 \end{column}
-\begin{column}{0.48\textwidth}
+\begin{column}{0.68\textwidth}
+\begin{center}
+\includegraphics[width=\textwidth]{../../buch/chapters/80-wahrscheinlichkeit/images/dreieck.pdf}
+\end{center}
 \end{column}
 \end{columns}
 \end{frame}
-- 
cgit v1.2.1