author: sijanec <sijanecantonluka@gmail.com> 2020-10-19 22:46:52 +0200
committer: sijanec <sijanecantonluka@gmail.com> 2020-10-19 22:46:52 +0200
commit: 60160f97fedef9f72f28eb7a8d88d157d68d87b2 (patch)
tree: e48c45b66d50f2dd021becff7b9a50f75df30058 /mat/domace_naloge/11
parent: OIV osnutek! (diff)
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10 files changed, 2481 insertions, 0 deletions
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diff --git a/mat/domace_naloge/11/dokument.out b/mat/domace_naloge/11/dokument.out
new file mode 100644
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--- /dev/null
+++ b/mat/domace_naloge/11/dokument.out
@@ -0,0 +1,3 @@
+\BOOKMARK [1][-]{section.1}{Ucbenik Matematika 2: Trikotnik \204 stran 33}{}% 1
+\BOOKMARK [1][-]{section.2}{Zakljucek}{}% 2
+\BOOKMARK [1][-]{section.3}{Razhro\235cevalne informacije}{}% 3
diff --git a/mat/domace_naloge/11/dokument.pdf b/mat/domace_naloge/11/dokument.pdf
new file mode 100644
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--- /dev/null
+++ b/mat/domace_naloge/11/dokument.pdf
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diff --git a/mat/domace_naloge/11/dokument.tex b/mat/domace_naloge/11/dokument.tex
new file mode 100644
index 0000000..6bf78f4
--- /dev/null
+++ b/mat/domace_naloge/11/dokument.tex
@@ -0,0 +1,271 @@
+% !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}{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}
+
+\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}{Trikotnik }
+\newcommand{\predmdn}{mat}
+\newcommand{\stevilkadn}{11}
+\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{19. 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 19. oktobra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učbenika. Kjer je bilo potrebno izbrati neke poljubne primere, sem jih vedno izbral naključno.
+\end{abstract}
+\tableofcontents
+
+\section{Učbenik \textit{Matematika 2}: Trikotnik --- stran 33}
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\setcounter{enumi}{6}
+	\item Načrtaj trikotnik s podatki: $c=\cm{4}, t_a=\cm{5,5}, \beta=\ang{120}$.
+		\begin{center}
+			\begin{tikzpicture}
+				\tkzDefPoint(0,0){A} \tkzDefPoint(4,0){B} \tkzDefPoint(5.5,0){AH}
+				\tkzInterLC(A,B)(B,A) \tkzGetPoints{AAGAIN}{AX} \tkzCompass(A,B)
+				\tkzDrawLine(A,AX) \tkzLabelLine[above, pos = 0.25](A,AX){$c$}			\tkzCompass(B,AX) \tkzInterCC(B,AX)(AX,B) \tkzGetPoints{CH}{USELESS}
+				\tkzCompass(B,CH) \tkzCompass(AX,CH)
+				\tkzDrawLine(B,CH) \tkzLabelLine[above left](B,CH){$a$}
+				\tkzInterLC(B,CH)(A,AH) \tkzGetPoints{HA}{USELESS}
+				\tkzCompass(A,HA) \tkzInterLC(B,CH)(HA,B) \tkzGetPoints{BAGAIN}{C}
+				\tkzCompass(HA,C) \tkzDrawLine(A,C) \tkzLabelLine[below](A,C){$b$}
+				\tkzDrawPoints(A) \tkzLabelPoints(A,B,C)
+			\end{tikzpicture}
+		\end{center}
+	\newpage
+	\item Načrtaj trikotnike.
+		\begin{multicols}{4}
+			\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
+				\item \color{codered} $$b=\cm{6}$$ $$v_b=\cm{4}$$ $$t_b=\cm{5}$$ % <&=&
+				\item \color{black} $$a=\cm{5}$$ $$v_a=\cm{3,5}$$ $$\gamma=\ang{75}$$
+				\item $$c=\cm{6}$$ $$a=\cm{4}$$ $$t_a=\cm{5,5}$$
+				\item $$b=\cm{5,5}$$ $$t_c=\cm{5}$$ $$\alpha=\ang{60}$$
+			\end{enumerate}
+		\end{multicols}
+		\begin{center}
+			\begin{tikzpicture}
+				\tkzDefPoint(0,0){A} \tkzDefPoint(69:6){C}
+				\tkzDefPoint(69:4){VH} \tkzDefPoint(69:-2){TH}
+				\tkzCompass(A,C) \tkzDrawLine(TH,C) \tkzLabelLine[below right](A,C){$b$}
+				\tkzDefMidPoint(A,C) \tkzGetPoint{ACM}
+				\tkzCompass(A,ACM) \tkzCompass(C,ACM)
+				\tkzDefMidPoint(A,ACM) \tkzGetPoint{AACMM}
+				\tkzInterLC(A,C)(A,AACMM) \tkzGetPoints{PH1}{PH2}
+				\tkzCompass(A,PH1) \tkzCompass(A,PH2)
+				\tkzInterCC(PH1,PH2)(PH2,PH1) \tkzGetPoints{USELESS}{V1}
+				\tkzCompass(PH1,V1)\tkzCompass(PH2,V1)
+				\tkzInterLC(A,V1)(A,VH) \tkzGetPoints{USELESS}{V}
+				\tkzCompass(A,V) \tkzInterLC(A,V)(V,V1) \tkzGetPoints{USELESS}{V1X}
+				\tkzDrawLine(A,V1X) \tkzCompass(V,V1X) \tkzInterCC(V1,V1X)(V1X,V1)
+				\tkzGetPoints{VP}{VPX} \tkzCompass(V1,VP) \tkzCompass(V1X,VP)
+				\tkzDrawLine(VPX,VP) \tkzInterLC(VP,VPX)(ACM,TH) \tkzGetPoints{USELE}{B}
+				\tkzCompass(ACM,B) \tkzDrawLine(B,C) \tkzLabelLine[below left](B,C){$a$}
+				\tkzDrawLine(A,B) \tkzLabelLine[above](A,B){$c$}
+				\tkzMarkRightAngles(PH1,A,V1 A,V,VP)
+				\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
+			\end{tikzpicture}
+		\end{center}
+	\item Načrtaj enakokraki trikotnik, katerega višina na osnovnico je dolga $\cm{3}$, kot ob osnovinci pa je velik $\ang{30}$.
+		\begin{center}
+			\begin{tikzpicture}
+				\tkzDefPoint(0,0){A} \tkzDefPoint(3,0){B}
+				\tkzDrawLine(A,B) \tkzLabelLine[above,pos=.4](A,B){$c$} \tkzCompass(A,B)
+				\tkzInterCC(A,B)(B,A) \tkzGetPoints{CL}{USELESS}
+				\tkzCompass(A,B) \tkzCompass(A,CL)
+				\tkzDefMidPoint(B,CL) \tkzGetPoint{K}\tkzCompass(B,K)\tkzCompass(CL,K)
+				\tkzDrawLine(A,K)
+				\tkzDefMidPoint(A,B) \tkzGetPoint{ABM} \tkzInterCC(A,B)(B,A)
+				\tkzGetPoints{ABP}{ABPX} \tkzCompass(A,ABP) \tkzCompass(B,ABP)
+				\tkzDrawLine(ABM,ABP) \tkzInterLL(ABPX,ABP)(A,K) \tkzGetPoint{C}
+				\tkzLabelLine[above left](A,C){$b$}
+				\tkzDrawLine(B,C) \tkzLabelLine[above right](B,C){$a$}
+				\tkzDrawPoints(A) \tkzLabelPoints(A)
+				\tkzLabelPoint[below left](B){$B$} \tkzLabelPoint[above left](C){$C$}
+			\end{tikzpicture}
+		\end{center}
+	\item Načrtaj pravokotni trikotnik s pravim kotom v oglišču $C$, katerega stranica $AC$ je dolga $\cm{4}$, simetrala kota pri $A$ pa $\cm{5}$. Nariši trikotniku včrtano krožnico.
+
+	Na tem mestu naj povem, da je \textbf{simetrala kota poltrak} in nima dolžine!
+	Zato trikotnika ne morem načrtati, zakar tudi včrtanje stranice ni možno. )-:
+		\if\false1
+			\begin{center}
+				\begin{tikzpicture}
+					\tkzDefPoint(0,0){A} \tkzDefPoint(69:4){C}
+					\tkzDrawLine(A,C) \tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
+					\tkz
+					\tkzDrawPoints(A) \tkzLabelPoints(A,C)
+				\end{tikzpicture}
+			\end{center}
+		\fi
+	\newpage
+	\item Načrtaj trikotnik in trikotniku očrtano krožnico.
+		\begin{multicols}{4}
+			\begin{enumerate}[label=\color{black}\textbf{\xslalph*)}]
+				\item $$a=\cm{5}$$ $$b=\cm{4}$$ $$\alpha=\ang{75}$$
+				\item \color{codered} $$b=\cm{3}$$ $$v_b=\cm{4}$$ $$\gamma=\ang{120}$$
+				\item \color{black} $$a=\cm{4}$$ $$b=\cm{5}$$ $$\gamma=\ang{90}$$
+				\item $$a=b=\cm{4}$$ $$c=6\cm$$
+			\end{enumerate}
+		\end{multicols}
+		\begin{center}
+			\begin{tikzpicture}
+				\tkzDefPoint(0,0){A} \tkzDefPoint(69:3){C} \tkzDefPoint(69:4){VHX}
+				\tkzLabelLine[above left](A,C){$b$} \tkzCompass(A,C)
+				\tkzInterLC(A,C)(C,A) \tkzGetPoints{A}{AX}
+				\tkzCompass(C,AX) \tkzDrawLine(A,AX) \tkzInterCC(AX,C)(C,AX)
+				\tkzGetPoints{BH}{BHX} \tkzCompass(AX,BH) \tkzCompass(C,BH)
+				\tkzDefMidPoint(A,C) \tkzGetPoint{ACM} \tkzCompass(A,ACM)
+				\tkzInterLC(A,C)(A,ACM) \tkzGetPoints{ACMX}{ACM} \tkzCompass(A,ACMX)
+				\tkzDrawLine(ACMX,AX)\tkzInterCC(ACMX,ACM)(ACM,ACMX) \tkzGetPoints{Y}{X}
+				\tkzCompass(ACM,X) \tkzCompass(ACMX,X)
+				\tkzInterLC(A,X)(A,VHX) \tkzGetPoints{USELESS}{VH}
+				\tkzCompass(A,VH) \tkzInterLC(A,X)(VH,A) \tkzGetPoints{A}{AXX}
+				\tkzCompass(VH,AXX) \tkzDrawLine(A,AXX)
+				\tkzInterCC(A,AXX)(AXX,A) \tkzGetPoints{V2}{V2X}
+				\tkzCompass(A,V2) \tkzCompass(AXX,V2) \tkzDrawLine(VH,V2)
+				\tkzInterLL(V2,V2X)(C,BH) \tkzGetPoint{B} \tkzDrawLine(C,B)
+				\tkzLabelLine[above left](C,B){$a$}
+				\tkzDrawLine(A,B) \tkzLabelLine[above left](A,B){$c$}
+				\tkzInterCC(C,B)(B,C) \tkzGetPoints{CBS}{CBSX} % krožnica
+				\tkzCompass(C,CBS) \tkzCompass(B,CBS) \tkzDrawLine(CBS,CBSX)
+				\tkzCompass(C,CBSX) \tkzCompass(B,CBSX)
+				\tkzInterCC(A,B)(B,A) \tkzGetPoints{ABS}{ABSX}
+				\tkzCompass(A,ABS) \tkzCompass(B,ABS) \tkzDrawLine(ABS,ABSX)
+				\tkzCompass(A,ABSX) \tkzCompass(B,ABSX)
+				\tkzInterLL(ABS,ABSX)(CBS,CBSX) \tkzGetPoint{S}
+				\tkzDrawPoints(A) \tkzLabelPoints(A,C,B)
+				\tkzMarkRightAngles(VH,A,C B,VH,A)
+				\tkzDrawCircle[fill = red!30,opacity=.3](S,A)
+				\tkzDrawPolygon[fill=blue!30,opacity=.3](A,B,C) % za razvidnost
+			\end{tikzpicture}
+		\end{center}
+\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 sekund.
+\fi
+%	\item $$$$
+\end{document}
diff --git a/mat/domace_naloge/11/dokument.toc b/mat/domace_naloge/11/dokument.toc
new file mode 100644
index 0000000..357860a
--- /dev/null
+++ b/mat/domace_naloge/11/dokument.toc
@@ -0,0 +1,3 @@
+\contentsline {section}{\numberline {1}Učbenik \textit {Matematika 2}: Trikotnik --- stran 33}{1}{section.1}%
+\contentsline {section}{\numberline {2}Zaključek}{3}{section.2}%
+\contentsline {section}{\numberline {3}Razhroščevalne informacije}{3}{section.3}%
diff --git a/mat/domace_naloge/11/stderr.log b/mat/domace_naloge/11/stderr.log
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author	sijanec <sijanecantonluka@gmail.com>	2020-10-19 22:46:52 +0200
committer	sijanec <sijanecantonluka@gmail.com>	2020-10-19 22:46:52 +0200
commit	60160f97fedef9f72f28eb7a8d88d157d68d87b2 (patch)
tree	e48c45b66d50f2dd021becff7b9a50f75df30058 /mat/domace_naloge/11
parent	OIV osnutek! (diff)
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