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diff --git a/mat/domace_naloge/10/dokument.tex b/mat/domace_naloge/10/dokument.tex new file mode 100644 index 0000000..be4edb7 --- /dev/null +++ b/mat/domace_naloge/10/dokument.tex @@ -0,0 +1,199 @@ +% !TeX encoding = UTF-8 +% !TeX spellcheck = sl_SI +% do-vimlatex-onwrite +\documentclass[]{article} +\usepackage[utf8]{inputenc} +\usepackage{etoolbox} +\usepackage[hidelinks]{hyperref} +\usepackage[a4paper, total={7in, 10in}]{geometry} +\usepackage{graphicx} +\usepackage{hologo} +\usepackage{amssymb} +\usepackage{pgfplots} +\usepackage[inline]{enumitem} +\usepackage{amsmath} +\usepackage{siunitx} +\usepackage{multicol} +\usepackage{tabularcalc} +\usepackage{amsmath} +\usepackage{float} +\usepackage{tasks} +\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 +\usepackage{xcolor} +\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}{0} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codegray}{rgb}{0.5,0.5,0.5} +\definecolor{codepurple}{rgb}{0.58,0,0.82} +\definecolor{backcolour}{rgb}{0.95,0.95,0.92} + +\lstdefinestyle{mystyle}{ + backgroundcolor=\color{backcolour}, + commentstyle=\color{codegreen}, + keywordstyle=\color{magenta}, + numberstyle=\tiny\color{codegray}, + stringstyle=\color{codepurple}, + basicstyle=\ttfamily\footnotesize, + breakatwhitespace=false, + breaklines=true, + captionpos=b, + keepspaces=true, + numbers=left, + numbersep=5pt, + showspaces=false, + showstringspaces=false, + showtabs=false, + tabsize=2 +} + +\lstset{style=mystyle} +\def\@maketitle{% + \newpage + \null + \vskip 2em% + \begin{center}% + \let \footnote \thanks + {\LARGE \@title \par}% + \vskip 1.5em% + {\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}{Krožnica, tetiva in tangenta } +\newcommand{\predmdn}{mat} +\newcommand{\stevilkadn}{10} +\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{16. 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} +% \end{abstract} +% \tableofcontents + +% \section{Učni list \textit{\snovdn}: osma naloga --- štirje primeri} +\begin{enumerate}[label=\textbf{\xslalph*)}] + \item Naj bosta $A$ in $B$ točki, ki sta oddaljeni \cm{5}. Nariši krožnico s polmerom \cm{7}, ki gre skozi točki $A$ in $B$. + \item Naj bo $A$ točka, ki je od premice $P$ oddaljena \cm{5}. Nariši krožnico s polmerom \cm{4}, ki gre skozi $A$ in se dotika $p$; + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(5,0){B} + \tkzDefPoint(-7,0){AH} \tkzDefPoint(12,0){BH} % namesto radija v intercc + \tkzDrawLine(A,B) \tkzCompass(A,B) + \tkzInterCC(A,AH)(B,BH) \tkzGetPoints{S}{S2} + \tkzCompass(A,S) \tkzCompass(B,S) \tkzDrawCircle(S,A) + \tkzCalcLength[cm](A,S) \tkzGetLength{dAS} + \tkzDrawSegment[dim={\pgfmathprintnumber\dAS cm,6pt,transform shape}](S,A) + \tkzDefPoint(0,4){PH1} \tkzDefPoint(1,4){PH2} + \tkzDrawLine(PH1,PH2) \tkzLabelLine[above](PH1,PH2){$p$} + \tkzMarkRightAngles(A,PH1,PH2) \tkzDrawLine(A,PH1) + \tkzDrawCircle(A,PH1) + \tkzDrawPoints(A) \tkzLabelPoints(A,B) + \end{tikzpicture} + \end{center} + \setcounter{enumi}{4} + \item Naj bosta $p$ in $q$ premici, ki oklepata kot \ang{60}, $A$ njuno presečišče in $B$ točka na premici $p$, ki je od $A$ oddaljena \cm{5}. Nariši krožnico, ki se dotika obeh premic, premice $p$ v točki $B$. + \item \color{magenta} Naj bosta $p$ in $q$ premici, ki oklepata kot \ang{30}, $A$ njuno presečišče in $B$ točka, na premici $p$, ki je od $A$ oddaljena \cm{5}. Nariši krožnico, ki se dotika premice $p$ v točki $B$, njeno središče pa leži na premici $q$. \color{black} Ta krožnica je enaka krožnici iz prejšnje naloge. + \begin{center} + \begin{tikzpicture} + \tkzDefPoint (0,0){A} \tkzDefPoint (5,0){B} + \tkzDefPoint(3.4,0){BH1} \tkzDefPoint(6.6,0){BH2} + \tkzCompass(A,B) \tkzCompass(B,BH1) \tkzCompass(B,BH2) + \tkzDrawLine[add = 0.2 and 0.4](A,B) \tkzLabelLine[above](A,B){$p$} + \tkzInterCC(A,B)(B,A) \tkzGetPoints{Q}{QX} + \tkzCompass(A,Q) \tkzCompass(B,Q) + \tkzDrawLine[add = 0.2 and 0.4](A,Q) \tkzLabelLine[above left](A,Q){$q$} + \tkzInterCC(BH1,BH2)(BH2,BH1) \tkzGetPoints{BP}{BPX} + \tkzCompass(BH1,BP) \tkzCompass(BH2,BP) + \tkzDrawLine(B,BP) \tkzMarkRightAngles(A,B,BP) + \tkzDefMidPoint(A,Q) \tkzGetPoint{AQM} \tkzDefMidPoint(AQM,Q) + \tkzGetPoint{AQMQM} \tkzInterLC(A,Q)(Q,AQMQM) \tkzGetPoints{QH1}{QH2} + \tkzCompass(Q,QH1) \tkzCompass(Q,QH2) + \tkzInterCC(QH1,QH2)(QH2,QH1) \tkzGetPoints{QPX}{QP} + \tkzCompass(QH1,QP)\tkzCompass(QH2,QP) + \tkzDrawLine[add = 0.2 and 0.4](Q,QP) \tkzMarkRightAngles(A,Q,QP) + \tkzInterLL(Q,QP)(B,BP) \tkzGetPoint{S} \tkzDrawCircle(S,Q) + \tkzDrawPoints(A) \tkzLabelPoints(A,B) \tkzMarkRightAngles(A,B,BP) + \tkzDrawLine[color=magenta](S,A) + \tkzLabelLine[color=magenta, above](S,A){$q$} + % \tkzInterLC(A,S)(B,S) \tkzGetPoints{RPH1}{RPH2} + % \tkzCompass[color=magenta](B,RPH1) \tkzCompass[color=magenta](B,RPH2) + % \tkzDefMidPoint(RPH1,RPH2) \tkzGetPoint{RP} + % \tkzCompass[color=magenta](RPH1,RP) \tkzCompass[color=magenta](RPH2,RP) + % \tkzDrawLine[color=magenta](RP,B) + \tkzDrawCircle[color=magenta](S,B) + % \tkzMarkRightAngles[color=magenta](A,RP,B) + \end{tikzpicture} + \end{center} +\end{enumerate} + +\section*{Zaključek} +Ta dokument obsega naloge, naročene dijakom 15. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učnega lista profesorja Domajnka. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno. + +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" +\fi +% \item $$$$ +\end{document} |