80 lines
2.7 KiB
TeX
80 lines
2.7 KiB
TeX
\documentclass{beamer}
|
|
\usepackage{polski}
|
|
\usepackage[utf8x]{inputenc}
|
|
\usepackage[T1]{fontenc}
|
|
\usepackage{amsmath}
|
|
\usepackage{graphicx}
|
|
\usepackage{tikz}
|
|
\title{Dowód twierdzenia Pitagorasa}
|
|
|
|
\author{Andrzej Kokosza}
|
|
|
|
\begin{document}
|
|
|
|
\begin{frame}
|
|
\titlepage
|
|
\end{frame}
|
|
\begin{frame}
|
|
\begin{center}
|
|
\begin{tikzpicture}
|
|
\draw [help lines] (0,0) grid(7,7);
|
|
\draw [fill=blue!50, opacity=0.5] (0,3) -- (0,0) -- (4,0);
|
|
\draw [fill=green!50, opacity=0.5] (4,0) -- (7,0) -- (7,4);
|
|
\draw [fill=red!50, opacity=0.5] (7,4) -- (7,7) -- (3,7);
|
|
\draw [fill=yellow!50, opacity=0.5] (3,7) -- (0,7) -- (0,3);
|
|
\draw [thick] (0,3) -- (4,0) -- (7,4) -- (3,7) -- (0,3);
|
|
\node at (2,-0.2) {a}; \node at (5.5,-0.2) {b}; \node at (7.2,2) {a}; \node at (7.2,5.5) {b};
|
|
\node at (1.5,7.2) {b}; \node at (5.,7.2) {a}; \node at (-0.2,1.5) {b}; \node at (-0.2,5) {a};
|
|
\node at (1.85, 1.85) {c}; \node at (5.15, 1.85) {c}; \node at (5.15,5.15) {c}; \node at (1.85, 5.15) {c};
|
|
\node at (3.5,3.5) {$c^2$};
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
\begin{center}
|
|
\begin{tikzpicture}
|
|
\draw [help lines] (0,0) grid(7,7);
|
|
\draw [fill=blue!50, opacity=0.5] (0,3) -- (0,0) -- (4,0);
|
|
\draw [fill=green!50, opacity=0.5] (0,3) -- (4,3) -- (4,0);
|
|
\draw [fill=red!50, opacity=0.5] (7,3) -- (7,7) -- (4,7);
|
|
\draw [fill=yellow!50, opacity=0.5] (7,3) -- (4,3) -- (4,7);
|
|
\node at (2,-0.2) {a}; \node at (-0.2,1.5) {b};
|
|
\node at (5.5,7.2) {b}; \node at (7.2,5) {a};
|
|
\node at (1.85, 1.85) {c}; \node at (5.15,5.15) {c};
|
|
\draw [thick] (0,3) rectangle (4,7);
|
|
\draw [thick] (4,0) rectangle (7,3);
|
|
\node at (2,5) {$a^2$}; \node at (5.5,1.5) {$b^2$};
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
\begin{center}
|
|
\begin{tikzpicture}
|
|
\draw [help lines] (0,0) grid(7,7);
|
|
\draw [fill=blue!50, opacity=0.7] (0,3) -- (0,0) -- (4,0);
|
|
\draw [fill=green!50, opacity=0.7] (4,0) -- (7,0) -- (7,4);
|
|
\draw [fill=red!50, opacity=0.7] (7,4) -- (7,7) -- (3,7);
|
|
\draw [fill=yellow!50, opacity=0.7] (3,7) -- (0,7) -- (0,3);
|
|
\draw [help lines] (0,0) grid(7,7);
|
|
\draw [fill=blue!50, opacity=0.7] (0,3) -- (0,0) -- (4,0);
|
|
\draw [fill=green!50, opacity=0.7] (0,3) -- (4,3) -- (4,0);
|
|
\draw [fill=red!50, opacity=0.7] (7,3) -- (7,7) -- (4,7);
|
|
\draw [fill=yellow!50, opacity=0.7] (7,3) -- (4,3) -- (4,7);
|
|
\draw [thick] (0,3) rectangle (4,7);
|
|
\draw [thick] (4,0) rectangle (7,3);
|
|
\draw [thick] (0,3) -- (4,0) -- (7,4) -- (3,7) -- (0,3);
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{frame}
|
|
|
|
\begin{frame}
|
|
\begin{center}
|
|
\begin{tikzpicture}
|
|
Oba kwadraty mają to samo pole powierzchni. Zauważmy, że kolorowe trójkąty w obu kwadratach mają tą samo pole powierzchni. Zatem pole białych kwadratów jest takie samo w obu, czyli
|
|
$$a^2+b^2=c^2$$
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
\end{frame}
|
|
\end{document} |