Geometrische Veranschaulichung der Dreiecksungleichung: ‖u+v‖ ≤ ‖u‖+‖v‖. Ideal für Vektoranalysis-Vorlesungen. Aus der technischen TikZ-Galerie von Sarmate (Quellen: MartinThoma/LaTeX-examples unter MIT, TeXample.net unter LPPL) — siehe auch unsere 900+ Figuren auf /tikz-gallery.php.
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes, calc, shapes, arrows}
\usepackage{amsmath,amssymb}
\usepackage{xcolor}
\definecolor{xvectorcolor}{HTML}{77933C}
\begin{document}
\begin{tikzpicture}[font=\boldmath]
\large
% Points
\coordinate (A) at (0,0) {};
\coordinate (B) at (5,0) {};
\coordinate (C) at (2,2) {};
% Draw the triangle
\path[fill=blue!10, fill=blue!5] (A) -- (B) -- (C) -- (A);
\draw[ultra thick, xvectorcolor, arrows={-latex}] (A) -- (C) node[sloped,midway,above=-0.1cm] {$x$};
\draw[ultra thick, blue!80, arrows={-latex}] (C) -- (B) node[sloped,midway,above=-0.1cm] {$y$};
\draw[ultra thick, red!80, arrows={-latex},line cap=round] (A) -- (B) node[sloped,midway,right=-0.3cm,above=-0.1cm] {$x+y$};
\end{tikzpicture}
\end{document}
