9 files changed, 1632 insertions, 0 deletions

diff --git a/mat/domace_naloge/2/a.out b/mat/domace_naloge/2/a.out
new file mode 100755
index 0000000..0fd74aa
--- /dev/null
+++ b/mat/domace_naloge/2/a.out
diff --git a/mat/domace_naloge/2/d=nx.c b/mat/domace_naloge/2/d=nx.c
new file mode 100644
index 0000000..8f91387
--- /dev/null
+++ b/mat/domace_naloge/2/d=nx.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+long long unsigned int d(long long unsigned int n) { return (n*(n-3))/2; }
+long long unsigned int x(long long unsigned int n) { return (n/2)-(3/2); }
+int main() {
+	long long unsigned int n = 3;
+	while (n < 420696969) {
+		if (d(n) != n*x(n)) {
+			fprintf(stdout, "%lld-kotnik! d(n)=%lld, x(n)=%lld, n*x=%lld\n", n, d(n), x(n), n*x(n));
+		}
+		n = n+2;
+	}
+}
+
diff --git a/mat/domace_naloge/2/dokument.aux b/mat/domace_naloge/2/dokument.aux
new file mode 100644
index 0000000..448b47d
--- /dev/null
+++ b/mat/domace_naloge/2/dokument.aux
@@ -0,0 +1,22 @@
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+\@writefile{lol}{\contentsline {lstlisting}{d=nx.c}{1}{lstlisting.-1}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}\protected@file@percent }
+\@writefile{toc}{\contentsline {section}{\numberline {3}Razhroščevalne informacije}{2}{section.3}\protected@file@percent }
diff --git a/mat/domace_naloge/2/dokument.log b/mat/domace_naloge/2/dokument.log
new file mode 100644
index 0000000..41064b9
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diff --git a/mat/domace_naloge/2/dokument.out b/mat/domace_naloge/2/dokument.out
new file mode 100644
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+++ b/mat/domace_naloge/2/dokument.out
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+\BOOKMARK [1][-]{section.1}{Ucbenik Matematika 2: Stran 11}{}% 1
+\BOOKMARK [1][-]{section.2}{Zakljucek}{}% 2
+\BOOKMARK [1][-]{section.3}{Razhro\235cevalne informacije}{}% 3
diff --git a/mat/domace_naloge/2/dokument.pdf b/mat/domace_naloge/2/dokument.pdf
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--- /dev/null
+++ b/mat/domace_naloge/2/dokument.pdf
diff --git a/mat/domace_naloge/2/dokument.synctex.gz b/mat/domace_naloge/2/dokument.synctex.gz
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+++ b/mat/domace_naloge/2/dokument.synctex.gz
diff --git a/mat/domace_naloge/2/dokument.tex b/mat/domace_naloge/2/dokument.tex
new file mode 100644
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+++ b/mat/domace_naloge/2/dokument.tex
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+\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{listings}
+\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{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{\stevilkadn}{2}
+\newcommand{\snovdn}{Konveksne množice }
+\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{8. september 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 8. septembra 2020, in njihove rešitve, ki sem jih spisal sam. Naloge obsegajo snov \textit{\snovdn}in so iz učbenika (stran 11). Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbral naključno.
+\end{abstract}
+\tableofcontents
+
+\section{Učbenik \textit{Matematika 2}: Stran 11} % 5, 7, 8, 6
+\begin{enumerate}[label=\textbf{\arabic*.}]
+	\setcounter{enumi}{4}
+	\item Kateri konveksni večkotnik ima 14 diagonal? % 5. naloga
+	
+	Število diagonal za konveksni $n$-kotnik izračunamo s funkcijo \texttt{ int d(int n) \{ return (n*(n-3))/2; \} } oziroma matematično $d=\frac{n(n-3)}{2}$. Če torej rešimo $14=\frac{n(n-3)}{2}$ za $n$, dobimo $n=7 \vee n=-4$. Mnogokotniki pa imajo lahko zgolj več kot dva kota, torej je odgovor sedemkotnik.
+		
+	\item Ali obstaja večkotnik, katerega število stranic je večkratnik števila diagonal?
+	
+	$n=\frac{n(n-3)}{2}$ rešimo za $n$ in dobimo $n=0 \vee n=5$. Zaradi enakega pravila, kot je opisano zgoraj, pa je edini možen rezultat petkotnik.
+	
+	\item Jaka je ugotovil, da je število diagonal nekega večkotnika enako večkratniku števila stranic tega večkotnika. Lina je trdila, da je takih večkotnikov nešteto. Ali ima prav?
+	
+	Najprej bi rad omenil, da je to vprašanje kratkomalo čudno, saj ne vemo, na koga se nanaša zadnji stavek. Odgovor bom napisal, kot da se nanaša na Lino.
+	
+	Enačbo $nx=\frac{n(n-3)}{2}$ lahko pretvorimo v $x=\frac{n}{2} - \frac{3}{2}$. Z dobljeno enačbo lahko za poljuben konveksen $n$-kotnik izračunamo faktor množenja, s katerim moramo pomnožiti $n$, da dobimo število diagonal. Torej ima Lina prav.
+	
+	Seveda je to dokaj logično, ker lahko dobimo vsako število, s tem da neko število zmnožimo z nekim drugim. Če pa imamo v mislih zgolj cela števila kot večkratnike, pa Lina nima prav, saj bo faktor množenja celo število samo, če je število stranic mnogokotnika liho.
+
+	Slednjo trditev lahko približno preverimo s programom tako, da poizkusimo vse mnogokotnike od trikotnika do 420696969-kotnika, ki imajo liho število stranic.
+	
+	\lstinputlisting[language=c]{d=nx.c}
+	
+	\item[\textbf{8.*}] Ali je presek dveh poljubnih konveksnih množic konveksna množica? Ali je unija dveh poljubnih konveksnih množic konveksna množica?
+	
+	Presek je, ker:
+	
+	$$ M = \text{konveksna} \wedge N = \text{konveksna} \wedge A, B \text{(poljubni)} \in M \cap N \rightarrow$$
+	$$ AB \subset M \wedge AB \subset N \rightarrow $$
+	$$ AB \subset M \cap N = \text{konveksna}$$
+	
+	Unija ni, ker, če sta $M$ in $N$ polravnini iste ravnine,
+	
+	$$ M = \text{polravnina} \wedge N = \text{polravnina} \wedge M \cup N \not= R \wedge A \in M \wedge B \in N \wedge A \cap B = \emptyset \rightarrow $$
+	$$ AB \setminus ( M \cup N ) \not= \emptyset $$
+\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 so 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/mat/domace_naloge/\stevilkadn/}{/mat/domace\_naloge/ \stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je  \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/mat/domace_naloge/\stevilkadn/dokument.pdf} in/ali \url{https://github.com/sijanec/sola-gimb-2/raw/master/mat/domace_naloge/\stevilkadn/dokument.pdf}.
+
+\if\razhroscevanje1
+\section{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Prej 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}
diff --git a/mat/domace_naloge/2/dokument.toc b/mat/domace_naloge/2/dokument.toc
new file mode 100644
index 0000000..9f953f1
--- /dev/null
+++ b/mat/domace_naloge/2/dokument.toc
@@ -0,0 +1,3 @@
+\contentsline {section}{\numberline {1}Učbenik \textit {Matematika 2}: Stran 11}{1}{section.1}%
+\contentsline {section}{\numberline {2}Zaključek}{2}{section.2}%
+\contentsline {section}{\numberline {3}Razhroščevalne informacije}{2}{section.3}%