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authorsijanec <sijanecantonluka@gmail.com>2020-09-09 21:35:07 +0200
committersijanec <sijanecantonluka@gmail.com>2020-09-09 21:35:07 +0200
commit4c5c55c0e7c5ba6231a347c63d86923e0e5f000e (patch)
treebc227d2b2115959d4e7bc77389ea923934d59f2a /mat
parentmat dn 1 "" => " za" (diff)
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Diffstat (limited to 'mat')
-rwxr-xr-xmat/domace_naloge/2/a.outbin0 -> 8392 bytes
-rw-r--r--mat/domace_naloge/2/d=nx.c13
-rw-r--r--mat/domace_naloge/2/dokument.aux22
-rw-r--r--mat/domace_naloge/2/dokument.log1421
-rw-r--r--mat/domace_naloge/2/dokument.out3
-rw-r--r--mat/domace_naloge/2/dokument.pdfbin0 -> 196173 bytes
-rw-r--r--mat/domace_naloge/2/dokument.synctex.gzbin0 -> 26585 bytes
-rw-r--r--mat/domace_naloge/2/dokument.tex170
-rw-r--r--mat/domace_naloge/2/dokument.toc3
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
Binary files differ
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
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+\@writefile{toc}{\contentsline {section}{\numberline {1}Učbenik \textit {Matematika 2}: Stran 11}{1}{section.1}\protected@file@percent }
+\@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
--- /dev/null
+++ b/mat/domace_naloge/2/dokument.log
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diff --git a/mat/domace_naloge/2/dokument.out 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
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diff --git a/mat/domace_naloge/2/dokument.tex 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}%