path: root/mat/domace_naloge/14/dokument.tex

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\usepackage{tabularcalc}
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\usepackage{filecontents}
\usepackage{textcomp}
\usepackage{tkz-euclide}
\usepackage{dirtytalk}
\usepackage{csquotes}
\usepackage{listings}
% \usepackage{multienum} % weird with labels
\usetikzlibrary{calc} %% not really needed............. idk.
%\usetikzlibrary{external}
% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
%\tikzexternalize
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\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
\newcommand{\razhroscevanje}{1}
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		{\LARGE \@title \par}%
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		{\large
			\lineskip .5em%
			\begin{tabular}[t]{c}% <------
				\@author%            <------ Authors
			\end{tabular}\par}%    <------
		\vskip 1em%
		{\large \@date}%
	\end{center}%
	\par
	\vskip 1.5em}
%opening
\newcommand{\snovdn}{Obodni in središčni kot }
\newcommand{\predmdn}{mat}
\newcommand{\stevilkadn}{14}
\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
\makeatletter
\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
\newcommand{\@xslalph}[1]{%
	\ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
	\or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
	\or t\or u\or v\or z\or \v{z}
	\else\@ctrerr\fi%
}
\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
\makeatother
\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
\newcommand*\textfrac[2]{
	\frac{\text{#1}}{\text{#2}}
}
\renewcommand\abstractname{Povzetek}
\date{26. oktober 2020}
\renewcommand\contentsname{Kazalo vsebine}
\renewcommand\figurename{Slika}
\renewcommand\abstractname{Povzetek}
\newcommand{\iic}{I\textsuperscript{2}C }
% \patchcmd{\thebibliography}{\section*{\refname}}{}{}{}
\title{%
	\snovdn --- \stevilkadn. domača naloga \\
	\large Matematika, Gimnazija Bežigrad}
\author{\begin{tabular}{rl}
		\textbf{Profesor:} & prof. Vilko Domajnko \\
		\textbf{Avtor:} & Anton Luka Šijanec, 2. a
%		\textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
\end{tabular}}


% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
\begin{document}
\maketitle

\begin{abstract}
Ta dokument obsega naloge, naročene dijakom 23. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka in vaj. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno.
\end{abstract}
\tableofcontents

\section{Vaje \textit{Matematika 2}: stran 29 --- Trikotnik}
\begin{enumerate}[label=\textbf{\arabic*.}]
	\setcounter{enumi}{165}
	\item[\textbf{166.*}] Načrtaj trikotnik $ABC$ z dano razliko dolžin stranic. Napiši postopek načrtovanja.
		\begin{enumerate}[label=\textbf{\xslalph*)}] % c b
			\setcounter{enumii}{1}
			\item $a-c=\cm{2}, \gamma=\ang{30}, v_a=\cm{4}$
				\input{166b.tex}
				\lstinputlisting[language=TeX]{166b.tex}
		\item $b-c=\cm{1}, \gamma=\ang{60}, a=\cm{3}$
			\input{166c.tex}
			\lstinputlisting[language=TeX]{166c.tex}
	\end{enumerate}
\end{enumerate}
\section{Učni list \textit{\snovdn}}
\begin{enumerate}[label=\textbf{\arabic*.}]
	\item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % b
		\begin{enumerate}[label=\textbf{\alph*)}]
			\setcounter{enumii}{1}
			\item $b=6, \alpha=\ang{30}, \beta=\ang{15}$
				\begin{figure}[!h]
					\makebox[\textwidth][c]{
						\begin{tikzpicture}
							\tkzDefPoint(0,0){A} \tkzDefPoint(6,0){K0}
							\tkzInterCC(A,K0)(K0,C) \tkzGetPoints{K60}{K60X}
							\tkzDefMidPoint(K60,K0) \tkzGetPoint{K30}
							\tkzInterLC(K30,A)(A,K0) \tkzGetPoints{C}{CX}
							\tkzInterLC(C,A)(C,A) \tkzGetPoints{AX}{AAGAIN}
							\tkzDrawLine(A,AX) \tkzLabelLine[above left](A,C){$b$}
							\tkzCompass(C,AX) \tkzCompass(A,K0) \tkzCompass(A,C)
							\tkzInterCC(C,AX)(AX,C) \tkzGetPoints{G60X}{G60}
							\tkzCompass(C,G60) \tkzCompass(AX,G60)
							\tkzDefMidPoint(AX,G60) \tkzGetPoint{G30}
							\tkzCompass(AX,G30) \tkzCompass(G60,G30)
							\tkzInterLC(C,G30)(C,AX) \tkzGetPoints{XX}{X}
							\tkzCompass(C,X) \tkzDrawLine(C,G30)
							\tkzDefMidPoint(X,G60) \tkzGetPoint{G45}
							\tkzCompass(X,G45) \tkzCompass(G60,G45)
							\tkzInterLL(C,G45)(A,K0) \tkzGetPoint{B}
							\tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$}
							\tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$}
							\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
							\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
						\end{tikzpicture}
					}
				\end{figure}
		\end{enumerate}
	\item Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
		\begin{enumerate}[label=\textbf{\alph*)}]
			\item $a=6, b=5, c=10$
				\begin{center}
					\begin{tikzpicture}
						\tkzDefPoint(0,0){A} \tkzDefPoint(10,0){B}
						\tkzDefPoint(5,0){bH} \tkzDefPoint(4,0){aH}
						\tkzDrawLine(A,B) \tkzLabelLine[below](A,B){$c$} \tkzCompass(A,B)
						\tkzInterCC(A,bH)(B,aH) \tkzGetPoints{C}{CX}
						\tkzCompass(A,C) \tkzCompass(B,C)
						\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$}
						\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
						\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
						\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
					\end{tikzpicture}
				\end{center}
		\end{enumerate}
	\if\false1
		\item[\textbf{*3.}] Načrtaj trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % ~c~=>b
		\setcounter{enumi}{3}
			\begin{enumerate}[label=\textbf{\alph*)}]
				\setcounter{enumii}{1}
				\item $c=8, a-b=2, \beta=\ang{60}$
					\begin{center}
						\begin{tikzpicture}
							\tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B}
							\tkzCompass(A,B) \tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
							\tkzInterCC(A,B)(B,A) \tkzGetPoints{aH}{aHX} \tkzDrawLine(B,aH)
							\tkzCompass(A,aH) \tkzCompass(B,aH)

							\tkzDrawPoints(A) \tkzLabelPoints(A,B)
						\end{tikzpicture}
					\end{center}
			\end{enumerate}
	\fi
	\item Načrtaj enakokraki trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % 2
		\begin{enumerate}[label=\textbf{\alph*)}]
			\setcounter{enumii}{1}
			\item $c=7, \gamma=\ang{30}$
				\begin{center}
					\begin{tikzpicture}
						\tkzDefPoint(0,0){A} \tkzDefPoint(7,0){B}
						\tkzDefMidPoint(A,B)\tkzGetPoint{M}\tkzCompass(A,M) \tkzCompass(B,M)
						\tkzInterLC(A,B)(B,M) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(B,AX)
						\tkzInterLC(A,B)(A,M) \tkzGetPoints{BX}{BAGAIN} \tkzCompass(A,BX)
						\tkzCompass(A,B) \tkzDrawLine[add=0 and 0](BX,AX) \tkzLabelLine[above](A,B){$c$}
						\tkzInterCC(A,BX)(BX,A) \tkzGetPoints{A60X}{A60}
						\tkzCompass(A,A60) \tkzCompass(BX,A60)
						\tkzInterCC(B,AX)(AX,B) \tkzGetPoints{B60}{B60X}
						\tkzCompass(B,B60) \tkzCompass(AX,B60)
						\tkzInterCC(A60,A)(A,A60) \tkzGetPoints{A120}{BXAGAIN}
						\tkzCompass(A,A120) \tkzCompass(A60,A120)
						\tkzInterCC(B60,B)(B,B60) \tkzGetPoints{AXAGAIN}{B120}
						\tkzCompass(B,B120) \tkzCompass(B60,B120)
						\tkzDefMidPoint(A60,A120) \tkzGetPoint{A90}
						\tkzInterLC(A,A90)(A,A120) \tkzGetPoints{A90CX}{A90C}
						\tkzCompass(A,A90C) \tkzDrawLine(A,A90C)
						\tkzDefMidPoint(B60,B120) \tkzGetPoint{B90}
						\tkzInterLC(B,B90)(B,B120) \tkzGetPoints{B90CX}{B90C}
						\tkzCompass(B,B90C) \tkzDrawLine(B,B90C)
						\tkzDefMidPoint(A120,A90C) \tkzGetPoint{A75}
						\tkzCompass(A120,A75) \tkzCompass(A90C,A75)
						\tkzDefMidPoint(B120,B90C) \tkzGetPoint{B75}
						\tkzCompass(B120,B75) \tkzCompass(B90C,B75)
						\tkzInterLL(A,A75)(B,B75) \tkzGetPoint{C}
						\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$}
						\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
						\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
						\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
					\end{tikzpicture}
				\end{center}
		\end{enumerate}
	\if\false1
		\item Načrtaj pravokotni trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
			\begin{enumerate}[label=\textbf{\alph*}]
				\item[\textbf{*b)}] $a+c=12, \alpha=\ang{60}$
			\end{enumerate}
	\fi
	\item[\textbf{*6.}] Načrtaj enakostranični trikotnik s podatki (vsi dolžinski podatki so v \cm{}): % a
		\begin{enumerate}[label=\textbf{\alph*)}]
			\item $a+v=10$
				\begin{figure}[H]
					\begin{tikzpicture}
						\tkzDefPoint(0,0){M} \tkzDefPoint(0,10){N}
						\tkzInterCC(M,N)(N,M) \tkzGetPoints{K60}{K60X}
						\tkzCompass(M,K60) \tkzCompass(N,K60) \tkzCompass(M,N)
						\tkzDefMidPoint(M,K60) \tkzGetPoint{K30}
						\tkzDrawLine(N,K30) \tkzInterLC(N,K30)(N,M) \tkzGetPoints{A4L}{K30C}
						\tkzCompass(N,K30C) \tkzDefMidPoint(K30C,M) \tkzGetPoint{K15}
						\tkzDefMidPoint(M,N) \tkzGetPoint{MN}
						\tkzCompass(M,MN) \tkzCompass(N,MN)
						\tkzInterLC(M,N)(M,MN) \tkzGetPoints{NX}{NAGAIN} \tkzCompass(M,NX)
						\tkzDrawLine(NX,N) \tkzLabelLine[above left](M,N){$v+a$}
						\tkzInterCC(MN,NX)(NX,MN) \tkzGetPoints{P}{R}
						\tkzInterLL(P,R)(N,K15)\tkzGetPoint{A}\tkzDrawLine[add=0 and 0](P,R)
						\tkzDrawLine(N,K15) \tkzInterCC(A,N)(N,A) \tkzGetPoints{AL}{L60}
						\tkzCompass(A,L60) \tkzCompass(N,L60)
						\tkzDefMidPoint(L60,N) \tkzGetPoint{L30} \tkzInterLC(A,L30)(A,N)
						\tkzGetPoints{L30CX}{L30C}\tkzCompass(A,L30C)\tkzDrawLine(A,L30)
						\tkzDefMidPoint(L30C,N) \tkzGetPoint{L15} \tkzDrawLine(A,L15)
						\tkzCompass(L30C,L15) \tkzCompass(N,L15)
						\tkzCompass(K60,K30) \tkzCompass(A,K30)
						\tkzCompass(N,L30) \tkzCompass(L60,L30)
						\tkzInterLL(M,N)(A,L15) \tkzGetPoint{C}
						\tkzInterLC(A,M)(M,A) \tkzGetPoints{AAGAIN}{B} \tkzCompass(M,B)
						\tkzDrawLine(C,B) \tkzLabelLine[above right](C,B){$a$}
						\tkzLabelLine[above left](C,A){$b$}
						\tkzLabelLine[above left](A,B){$c$}
						\tkzDrawPolygon[fill=blue!30, opacity=.30](A,B,C)
						\tkzDrawPoints(M) \tkzLabelPoints(A,C,B) \tkzMarkRightAngles(P,M,N)
					\end{tikzpicture}
				\end{figure}
		\end{enumerate}
\end{enumerate}
\section{Zaključek}
Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
\hologo{LaTeX}
izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo mojem šolskem Git repozitoriju na
\url{https://github.com/sijanec/sola-gimb-2} v mapi 
\href{https://github.com/sijanec/sola-gimb-2/tree/master/\predmdn/domace_naloge/\stevilkadn/}{/\predmdn/domace\_naloge/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je  \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/\predmdn/domace_naloge/\stevilkadn/dokument.pdf}.

\if\razhroscevanje1
\section{Razhroščevalne informacije}
Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.

Grafi imajo natančnost \functionSamples\space točk na graf.

Konec generiranja dokumenta: \input|"date -Ins"

Dokument se je generiral aaasecgeninsaaa \SI{}{\second}.
\fi
%	\item $$$$
\end{document}