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diff --git a/mat/domace_naloge/18/dokument.tex b/mat/domace_naloge/18/dokument.tex new file mode 100644 index 0000000..2a7f51f --- /dev/null +++ b/mat/domace_naloge/18/dokument.tex @@ -0,0 +1,246 @@ +% !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{calculator} +\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[ddMMyyyy]{datetime} +\usepackage{ccicons} +\usepackage{chemformula} +\usepackage{gensymb} +\usepackage[normalem]{ulem} +\usepackage[slovene]{babel} +\usepackage{cancel} +% \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}{1} +\definecolor{codegreen}{rgb}{0,0.6,0} +\definecolor{codered}{rgb}{1,0,0} +\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} +\renewcommand{\dateseparator}{. } +\settimeformat{hhmmsstime} +\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}{Steinerjev problem } +\newcommand{\predmdn}{mat} +\newcommand{\stevilkadn}{18} +\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{17. november 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}} +\newcommand\hcancel[2][black]{\setbox0=\hbox{$#2$}% +\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2} +% \everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260 +\begin{document} +\maketitle +\begin{abstract} +Ta dokument vsebuje domačo nalogo vključujoč snov \textit{\snovdn}, ki nam jo je bil profesor naročil 27. novembra 2020, in njene rešitve, ki sem jih spisal sam. Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih izbral tako, da mi je bilo delo najlažje. +\end{abstract} +\tableofcontents +\section{Učni list \textit{\snovdn}} +\begin{enumerate}[label=\textbf{\arabic*.}] + %\setcounter{enumi}{2} + %\item V vasi A je 45 šolarjev, v vasi B živi 30 šolarjev, v vasi C pa 15 šolarjev. Za vse skupaj nameravajo postaviti novo šolo. Kako naj postavijo šolo, da bo skupna dolžina poti, ki jo morajo ti šolarji napraviti od šoledo doma, najmanjša? + + %Skupna pot učencev za kraj $Š$ je: + + %$$|AŠ|\cdot45+|BŠ|\cdot30+|CŠ|\cdot15$$ + + %Šola naj bo v kraju A. + \item Načrtaj trikotnik s stranicami \SI{6}{\centi\meter}, \cm{7} in \cm{8} in mu vriši Steinerjevo (oz. Fermantovo) točko. + \begin{center} + \begin{tikzpicture} + \tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B} + \tkzDefPoint(7,0){bH} \tkzDefPoint(8-6,0){aH} + \tkzInterCC(A,bH)(B,aH) \tkzGetPoints{C}{CX} + \tkzDrawPolygon[fill=red!30, opacity=0.3](A,B,C) + \tkzCompass(B,bH) \tkzCompass(A,aH) + \tkzInterCC(A,aH)(aH,A) \tkzGetPoints{L6X}{L6} + \tkzCompass(A,L6) \tkzCompass(aH,L6) + \tkzDefMidPoint(L6,aH) \tkzGetPoint{L3} + \tkzCompass(L6,L3) \tkzCompass(aH,L3) + \tkzInterCC(B,bH)(bH,B) \tkzGetPoints{R6}{R6X} + \tkzCompass(B,R6) \tkzCompass(bH,R6) + \tkzDefMidPoint(R6,bH) \tkzGetPoint{R3} + \tkzCompass(R6,R3) \tkzCompass(bH,R3) + \tkzInterLL(A,L3)(B,R3) \tkzGetPoint{S1} + \tkzDrawLine(A,S1) \tkzDrawLine(B,S1) + \tkzDefMidPoint(C,B) \tkzGetPoint{CB} + \tkzCompass(C,CB) \tkzCompass(B,CB) + \tkzInterCC(B,CB)(CB,B) \tkzGetPoints{B6X}{B6} + \tkzCompass(B,B6) \tkzCompass(CB,B6) + \tkzDefMidPoint(CB,B6) \tkzGetPoint{B3} + \tkzCompass(CB,B3) \tkzCompass(B6,B3) + \tkzInterCC(C,CB)(CB,C) \tkzGetPoints{C6}{C6X} + \tkzCompass(C,C6) \tkzCompass(CB,C6) + \tkzDefMidPoint(CB,C6) \tkzGetPoint{C3} + \tkzCompass(CB,C3) \tkzCompass(C6,C3) + \tkzInterLL(B,B3)(C,C3) \tkzGetPoint{S2} + \tkzDrawLine(B,S2) \tkzDrawLine(C,S2) + \tkzInterCC(S1,A)(S2,B) \tkzGetPoints{M}{MX} + \tkzCompass(S1,M) \tkzCompass(S2,M) + \tkzCalcLength[cm](A,M)\tkzGetLength{AMl} + \tkzCalcLength[cm](B,M)\tkzGetLength{BMl} + \tkzCalcLength[cm](C,M)\tkzGetLength{CMl} + \tkzDrawSegment[dim={\pgfmathprintnumber\AMl,0pt,transform shape}](A,M) + \tkzDrawSegment[dim={\pgfmathprintnumber\BMl,0pt,transform shape}](M,B) + \tkzDrawSegment[dim={\pgfmathprintnumber\CMl,0pt,transform shape}](M,C) + \tkzDrawPoints(A,B,C,S1,S2,M) \tkzLabelPoints(A,B,C,S1,S2,M) + % \tkzDrawPoints[color=red](aH,bH) \tkzLabelPoints[color=red](aH,bH) + \end{tikzpicture} + \end{center} + $$d\ \Tilde=\ 5,15+2,82+4,07=12,04$$ + \setcounter{enumi}{2} + \item Denimo, da so $A$, $B$, $C$ in $D$ točke v ogliščih pravokotnika s stranicama dolžine \cm{6} in \cm{10}. Poišči najkrajšo povezavo s sistemom poti med temi štirimi točkami. + \begin{center} + \begin{tikzpicture}[scale=.7] + \tkzDefPoint(0,0){A} \tkzDefPoint(10,0){B} + \tkzDefPoint(10,6){C} \tkzDefPoint(0,6){D} + \tkzDrawPolygon[fill=red!30, opacity=.3](A,B,C,D) + \tkzInterCC(B,C)(C,B) \tkzGetPoints{EX}{E} + \tkzCompass(B,E) \tkzCompass(C,E) + \tkzInterCC(A,D)(D,A) \tkzGetPoints{F}{FX} + \tkzCompass(A,F) \tkzCompass(D,F) + \tkzDefMidPoint(B,E) \tkzGetPoint{BE} + \tkzCompass(B,BE) \tkzCompass(E,BE) + \tkzDefMidPoint(C,E) \tkzGetPoint{CE} + \tkzCompass(C,CE) \tkzCompass(E,CE) + \tkzDrawLine(C,BE) \tkzDrawLine(B,CE) + \tkzInterLL(B,CE)(C,BE) \tkzGetPoint{SE} + \tkzDrawLine(E,F) \tkzInterLC(E,F)(SE,B) \tkzGetPoints{GX}{G} + \tkzCompass(SE,G) + \tkzDefMidPoint(A,F) \tkzGetPoint{AF} + \tkzCompass(A,AF) \tkzCompass(F,AF) + \tkzDefMidPoint(D,F) \tkzGetPoint{DF} + \tkzCompass(D,DF) \tkzCompass(F,DF) + \tkzDrawLine(D,AF) \tkzDrawLine(A,DF) + \tkzInterLL(A,DF)(D,AF) \tkzGetPoint{SF} + \tkzInterLC(E,F)(SF,A) \tkzGetPoints{H}{HX} + \tkzCompass(SF,H) + \tkzCalcLength[cm](A,H)\tkzGetLength{AHl} + \tkzCalcLength[cm](B,G)\tkzGetLength{BGl} + \tkzCalcLength[cm](C,G)\tkzGetLength{CGl} + \tkzCalcLength[cm](D,H)\tkzGetLength{DHl} + \tkzCalcLength[cm](G,H)\tkzGetLength{GHl} + \tkzDrawSegment[dim={\pgfmathprintnumber\AHl,0pt,transform shape}](A,H) + \tkzDrawSegment[dim={\pgfmathprintnumber\BGl,0pt,transform shape}](G,B) + \tkzDrawSegment[dim={\pgfmathprintnumber\CGl,0pt,transform shape}](G,C) + \tkzDrawSegment[dim={\pgfmathprintnumber\DHl,0pt,transform shape}](D,H) + \tkzDrawSegment[dim={\pgfmathprintnumber\GHl,0pt,transform shape}](H,G) + \tkzDrawPoints(A,B,C,D,G,H) \tkzLabelPoints(A,B,C,D,G,H) + \end{tikzpicture} + \end{center} + $$d\ \tilde=\ 3,46\cdot4+6,54=20,38$$ +\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 v mojem šolskem Git repozitoriju na +\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi +\href{https://git.sijanec/sola-gimb-2/src/branch/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://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/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: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins" + +Dokument se je generiral R0qK1KR2 \SI{}{\second}. +\fi +% \item $$$$ aaasecgeninsaaa R0qK1KR2 +\end{document} |