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Diffstat (limited to 'mat')
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diff --git a/mat/domace_naloge/1/dokument-figure0.dep b/mat/domace_naloge/1/dokument-figure0.dep new file mode 100644 index 0000000..7c5b760 --- /dev/null +++ b/mat/domace_naloge/1/dokument-figure0.dep @@ -0,0 +1 @@ +dokument-figure0.pdf: dokument-figure0.pgf-plot.table diff --git a/mat/domace_naloge/1/dokument-figure0.dpth b/mat/domace_naloge/1/dokument-figure0.dpth new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/mat/domace_naloge/1/dokument-figure0.dpth diff --git a/mat/domace_naloge/1/dokument-figure0.log b/mat/domace_naloge/1/dokument-figure0.log new file mode 100644 index 0000000..fe5df7b --- /dev/null +++ b/mat/domace_naloge/1/dokument-figure0.log @@ -0,0 +1,1898 @@ +This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2020.5.18) 8 SEP 2020 22:33 +entering extended mode + \write18 enabled. + %&-line parsing enabled. +**\def\tikzexternalrealjob{dokument}\input{dokument} +(./dokument.tex 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defining Unicode char U+0111 (decimal 273) + defining Unicode char U+0112 (decimal 274) + defining Unicode char U+0113 (decimal 275) + defining Unicode char U+0114 (decimal 276) + defining Unicode char U+0115 (decimal 277) + defining Unicode char U+0116 (decimal 278) + defining Unicode char U+0117 (decimal 279) + defining Unicode char U+0118 (decimal 280) + defining Unicode char U+0119 (decimal 281) + defining Unicode char U+011A (decimal 282) + defining Unicode char U+011B (decimal 283) + defining Unicode char U+011C (decimal 284) + defining Unicode char U+011D (decimal 285) + defining Unicode char U+011E (decimal 286) + defining Unicode char U+011F (decimal 287) + defining Unicode char U+0120 (decimal 288) + defining Unicode char U+0121 (decimal 289) + defining Unicode char U+0122 (decimal 290) + defining Unicode char U+0123 (decimal 291) + defining Unicode char U+0124 (decimal 292) + defining Unicode char U+0125 (decimal 293) + defining Unicode char U+0128 (decimal 296) + defining Unicode char U+0129 (decimal 297) + defining Unicode char U+012A (decimal 298) + defining Unicode char U+012B (decimal 299) + defining Unicode char U+012C (decimal 300) + defining Unicode char U+012D (decimal 301) + defining Unicode char U+012E (decimal 302) + defining Unicode char U+012F (decimal 303) + defining Unicode char U+0130 (decimal 304) + defining Unicode char U+0131 (decimal 305) + defining Unicode char U+0132 (decimal 306) + defining Unicode char U+0133 (decimal 307) + defining Unicode char U+0134 (decimal 308) + defining Unicode char U+0135 (decimal 309) + defining Unicode char U+0136 (decimal 310) + defining Unicode char U+0137 (decimal 311) + defining Unicode char U+0139 (decimal 313) + defining Unicode char U+013A (decimal 314) + defining Unicode char U+013B (decimal 315) + defining Unicode char U+013C (decimal 316) + defining Unicode char U+013D (decimal 317) + defining Unicode char U+013E (decimal 318) + defining Unicode char U+0141 (decimal 321) + defining Unicode char U+0142 (decimal 322) + defining Unicode char U+0143 (decimal 323) + defining Unicode char U+0144 (decimal 324) + defining Unicode char U+0145 (decimal 325) + defining Unicode char U+0146 (decimal 326) + defining Unicode char U+0147 (decimal 327) + defining Unicode char U+0148 (decimal 328) + defining Unicode char U+014A (decimal 330) + defining Unicode char U+014B (decimal 331) + defining Unicode char U+014C (decimal 332) + defining Unicode char U+014D (decimal 333) + defining Unicode char U+014E (decimal 334) + defining Unicode char U+014F (decimal 335) + defining Unicode char U+0150 (decimal 336) + defining Unicode char U+0151 (decimal 337) + defining Unicode char U+0152 (decimal 338) + defining Unicode char U+0153 (decimal 339) + defining Unicode char U+0154 (decimal 340) + defining Unicode char U+0155 (decimal 341) + defining Unicode char U+0156 (decimal 342) + defining Unicode char U+0157 (decimal 343) + defining Unicode char U+0158 (decimal 344) + defining Unicode char 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482) + defining Unicode char U+01E3 (decimal 483) + defining Unicode char U+01E6 (decimal 486) + defining Unicode char U+01E7 (decimal 487) + defining Unicode char U+01E8 (decimal 488) + defining Unicode char U+01E9 (decimal 489) + defining Unicode char U+01EA (decimal 490) + defining Unicode char U+01EB (decimal 491) + defining Unicode char U+01F0 (decimal 496) + defining Unicode char U+01F4 (decimal 500) + defining Unicode char U+01F5 (decimal 501) + defining Unicode char U+0218 (decimal 536) + defining Unicode char U+0219 (decimal 537) + defining Unicode char U+021A (decimal 538) + defining Unicode char U+021B (decimal 539) + defining Unicode char U+0232 (decimal 562) + defining Unicode char U+0233 (decimal 563) + defining Unicode char U+1E02 (decimal 7682) + defining Unicode char U+1E03 (decimal 7683) + defining Unicode char U+200C (decimal 8204) + defining Unicode char U+2010 (decimal 8208) + defining Unicode char U+2011 (decimal 8209) + defining Unicode char U+2012 (decimal 8210) 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set format "%.5f" +set format "%.7e";; set datafile separator ","; plot "ocene.csv" using 1:2 every 1; diff --git a/mat/domace_naloge/1/dokument.pgf-plot.table b/mat/domace_naloge/1/dokument.pgf-plot.table new file mode 100644 index 0000000..40d1547 --- /dev/null +++ b/mat/domace_naloge/1/dokument.pgf-plot.table @@ -0,0 +1,15 @@ + +# Curve 0 of 1, 10 points +# Curve title: ""ocene.csv" using 1:2 every 1" +# x y type +1.5000000e+00 3.0000000e+00 i +2.0000000e+00 3.0000000e+00 i +3.0000000e+00 4.0000000e+00 i +1.0000000e+00 1.0000000e+00 i +2.5000000e+00 3.0000000e+00 i +4.0000000e+00 5.0000000e+00 i +3.5000000e+00 4.0000000e+00 i +5.0000000e+00 5.0000000e+00 i +4.0000000e+00 4.0000000e+00 i +2.0000000e+00 2.0000000e+00 i + diff --git a/mat/domace_naloge/1/dokument.synctex.gz b/mat/domace_naloge/1/dokument.synctex.gz Binary files differnew file mode 100644 index 0000000..10bdb6c --- /dev/null +++ b/mat/domace_naloge/1/dokument.synctex.gz diff --git a/mat/domace_naloge/1/dokument.tex b/mat/domace_naloge/1/dokument.tex new file mode 100644 index 0000000..7194af5 --- /dev/null +++ b/mat/domace_naloge/1/dokument.tex @@ -0,0 +1,260 @@ +\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} +\usetikzlibrary{calc} %% not really needed............. idk. +%\usetikzlibrary{external} +\usetkzobj{all} +%\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} +\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}{1} +\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{% + Osnovni geometrijski pojmi --- \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{Osnovni geometrijski pojmi} 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} % 7, 2, 4, 5 +\begin{enumerate}[label=\textbf{\arabic*.}] + \setcounter{enumi}{1} + \item Na ravnini nariši vzporedni premici $p$ in $q$. Nariši še dve premici tako, da bodo vse štiri premice razdelile ravnino na čim več delov. Koliko večkotnikov lahko oblikuješ na ta način? Katere? % 2. naloga + + \begin{center} + + \begin{tikzpicture} % [scale=1] + % \tkzInit[xmin=-6,ymin=-4,xmax=6,ymax=6] + \tkzDefPoint(0,1){A} + \tkzDefPoint(6,1){B} + \tkzDefPoint(4,1){C} + % \tkzDefPoint(0,0){D} + \tkzDefPoint(3,0){S} + % \tkzDefLine[mediator](A,B) + % \tkzDefLine[mediator](C,D) + \tkzDrawLine[mediator, add = .5 and 1](A,S) \tkzLabelLine[above](A,S){$r$} % add = 1 and 1 + \tkzDrawLine[mediator](B,S) \tkzLabelLine[below](B,S){$s$} + \tkzDrawLine[mediator](A,B) \tkzLabelLine[below](A,B){$a$} + \tkzDefLine[bisector](S,C,B) + \tkzGetPoint{b} + \tkzDrawLine[color=black](C,b) + \tkzLabelLine[right](C,b){$b$} + % \tkzDefPointOnLine[pos=1.2](A,B) % dodano v 2018! + % \tkzGetPoint{P} + % \tkzInterLL(A,C)(B,D) \tkzGetPoint{I} + + % \tkzDrawPolygon (A,B,C,D) + % \tkzDrawSegments(A,C B,D) + % \tkzMarkRightAngles[fill=Maroon!20,size=.3,opacity=.5](D,A,B A,B,C B,C,D C,D,A) + \tkzDrawPoints(A,B,S,C) + + % \tkzMarkSegments[mark=s||](I,A I,B I,C I,D) + % \tkzLabelPoints(C,D) + % \tkzLabelPoints[above=6pt](I) + \tkzLabelPoints[above right](A,B,S,C) + + \end{tikzpicture} + \end{center} + + Oblikujem lahko dva trikotnika in en štirikotnik in s tem ravnino razdelim na največ enajst delov. + + \setcounter{enumi}{3} + \item Alja je premice $p$, $q$ in $r$ ravnine $\Pi$ zapisala: $p \cap q = \emptyset$ in $q \cap r = {A}$. Kaj lahko sklepaš o medsebojni legi premic $p$, $q$ in $r$? + + $$ ( p\parallel q \wedge r \cap p \not= \emptyset ) \vee ( p = q \wedge r \cap p = {A} ) $$ + + \item Dan je kvader $ABCDEFGH$. Napiši vsaj pet dvojic vzporednih premic in vsaj pet dvojic mimobežnih premic, ki jih določajo oglišča kvadra. + + $$ \text{vzporednice:} \space (A,B)\parallel(C,D) ; (B,C)\parallel(D,A) ; (E,F)\parallel(G,H) ; (F,G)\parallel(H,E) ; (A,B)\parallel(E,F) $$ + + $$ \text{mimobežince:} \space (A,B) \nparallel (C,E) ; (C,D) \nparallel (A,G) ; (B,C) \nparallel (D,F) ; (D,A) \nparallel (B,H) ; (E,F) \nparallel (G,A)$$ + + \setcounter{enumi}{6} + \item Dana je kocka $ABCDEFGH$. + \begin{enumerate}[label=\textbf{\xslalph*)}] + \item Izmed oglišč izberi vsaj pet trojic nekolinearnih točk. Za vsako trojico točk nariši ustrezno skico in ugotovi, kakšen trikotnik določajo. + + \begin{multicols}{3} + + \begin{itemize} + \item $ (A, B, C) $ --- pravokotnega + + \begin{tikzpicture} + \tkzDefPoint(0,0){A} + \tkzDefPoint(0,1){B} + \tkzDefPoint(1,1){C} + \tkzDrawLine[add = 0 and 0](A,B) + \tkzDrawLine[add = 0 and 0](B,C) + \tkzDrawLine[add = 0 and 0](C,A) + \tkzDrawPoints(A,B,C) + \tkzLabelPoints[above left](B) + \tkzLabelPoints[below right](A) + \tkzLabelPoints[above right](C) + \tkzMarkRightAngles[fill=gray!20,size=.3,opacity=.5](A,B,C) + \end{tikzpicture} + + \item $ (B, C, D) $ --- pravokotnega + + \begin{tikzpicture} + \tkzDefPoint(0,1){D} + \tkzDefPoint(1,0){B} + \tkzDefPoint(1,1){C} + \tkzDrawLine[add = 0 and 0](D,B) + \tkzDrawLine[add = 0 and 0](B,C) + \tkzDrawLine[add = 0 and 0](C,D) + \tkzDrawPoints(D,B,C) + \tkzLabelPoints[below right](B) + \tkzLabelPoints[above right](C) + \tkzLabelPoints[above left](D) + \tkzMarkRightAngles[fill=gray!20,size=.3,opacity=.5](B,C,D) + \end{tikzpicture} + + \item $ (C, D, A) $ --- pravokotnega + + \begin{tikzpicture} + \tkzDefPoint(0,1){D} + \tkzDefPoint(0,0){A} + \tkzDefPoint(1,1){C} + \tkzDrawLine[add = 0 and 0](D,A) + \tkzDrawLine[add = 0 and 0](A,C) + \tkzDrawLine[add = 0 and 0](C,D) + \tkzDrawPoints(D,A,C) + \tkzLabelPoints[below left](A) + \tkzLabelPoints[above right](C) + \tkzLabelPoints[above left](D) + \tkzMarkRightAngles[fill=gray!20,size=.3,opacity=.5](A,D,C) + \end{tikzpicture} + + \item $ (F, A, E) $ --- pravokotnega + + \begin{tikzpicture} + \tkzDefPoint(0,0){E} + \tkzDefPoint(0,1){A} + \tkzDefPoint(1,0){F} + \tkzDrawLine[add = 0 and 0](E,A) + \tkzDrawLine[add = 0 and 0](A,F) + \tkzDrawLine[add = 0 and 0](F,E) + \tkzDrawPoints(E,A,F) + \tkzLabelPoints[above left](A) + \tkzLabelPoints[below right](F) + \tkzLabelPoints[below left](E) + \tkzMarkRightAngles[fill=gray!20,size=.3,opacity=.5](A,E,F) + \end{tikzpicture} + + \item $ (D, A, F) $ --- pravokotnega + + \begin{tikzpicture} + \tkzDefPoint(1,1){D} + \tkzDefPoint(0,1){A} + \tkzDefPoint(0,0){F} + \tkzDrawLine[add = 0 and 0](D,A) + \tkzDrawLine[add = 0 and 0](A,F) + \tkzDrawLine[add = 0 and 0](F,D) + \tkzDrawPoints(D,A,F) + \tkzLabelPoints[above left](A) + \tkzLabelPoints[below left](F) + \tkzLabelPoints[above right](D) + \tkzMarkRightAngles[fill=gray!20,size=.3,opacity=.5](D,A,F) + \end{tikzpicture} + + \item[\vspace{\fill}] + + % $$ (A, B, C) ; (B, C, D); (C, D, A) ; (F, A, E) ; (D, A, F) $$ + \end{itemize} + + \end{multicols} + + \item Ali lahko k vsaki tako izbrani trojici oglišč dodaš oglišče, da so v dobljeni četverici nekoplanarne točke? Zapiši ustrezne četverice. + + $$ (A, B, C, E) ; (B, C, D, E) ; (C, D, A, E) ; (F, A, E, D) ; (D, A, F, E) $$ + \end{enumerate} +\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/1/dokument.toc b/mat/domace_naloge/1/dokument.toc new file mode 100644 index 0000000..5e44770 --- /dev/null +++ b/mat/domace_naloge/1/dokument.toc @@ -0,0 +1,3 @@ +\contentsline {section}{\numberline {1}U\IeC {\v c}benik \textit {Matematika 2}: Stran 11}{1}{section.1} +\contentsline {section}{\numberline {2}Zaklju\IeC {\v c}ek}{2}{section.2} +\contentsline {section}{\numberline {3}Razhro\IeC {\v s}\IeC {\v c}evalne informacije}{2}{section.3} diff --git a/mat/domace_naloge/1/ocene.csv b/mat/domace_naloge/1/ocene.csv new file mode 100644 index 0000000..5e043fb --- /dev/null +++ b/mat/domace_naloge/1/ocene.csv @@ -0,0 +1,14 @@ +%% LaTeX2e file `ocene.csv' +%% generated by the `filecontents' environment +%% from source `dokument' on 2020/09/08. +%% +1.5,3 +2,3 +3,4 +1,1 +2.5,3 +4,5 +3.5,4 +5,5 +4,4 +2,2 |