diff --git a/zajecia 3/ragdoll.pdf b/zajecia 3/ragdoll.pdf deleted file mode 100644 index 40cb8bd..0000000 Binary files a/zajecia 3/ragdoll.pdf and /dev/null differ diff --git a/zajecia 4/zadania03.txt b/zajecia 4/zadania03.txt new file mode 100644 index 0000000..9eac552 --- /dev/null +++ b/zajecia 4/zadania03.txt @@ -0,0 +1,15 @@ +#+TITLE: Pakiety matematyczne: amsmath, amsthm, mathtools − prezentacja możliwości + +* Prezentacja podczas zajęć +W czasie prezentacji należy omówić: + + pakiet amsmath − wyrównywania wzorów wystawionych, wielopoziomowe + indeksy np. w sumach, komenda \operatorname + + pakiet amsthm − sposoby ddefiniowania nowych środowisk typu + twierdzenie, definicja; opcjonalny argument środowiska; polecenie + \theoremstyle + + pakiet mathtools − komenda \smashoperator; otoczenie typu matrix i + pochodne; komenda \DeclarePairedDelimiter; komenda showonlyrefs + +* Zadanie do wykonania podczas zajęć + + Przetestować omówione podczas prezentacji możliwości pakietów na + 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index 0000000..881789a Binary files /dev/null and b/zajecia 4/zajecia03-plik.synctex.gz differ diff --git a/zajęcia 5/main.tex b/zajęcia 5/main.tex new file mode 100644 index 0000000..64fed96 --- /dev/null +++ b/zajęcia 5/main.tex @@ -0,0 +1,80 @@ +\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} \ No newline at end of file