%
%	gbb60166@gmail.com	https://unilab.gbb60166.jp/prekou/prekou.htm
%
% aspectratio= は 1610, 169, 149, 54, 32 の中から選べる（省略時は 43）
% C:\texlive\2024\texmf-dist\tex\latex\beamer\beamer.cls
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfpagemode=FullScreen},aspectratio=169]{beamer}
%\documentclass[20pt,dvipdfmx,usepdftitle=false,hyperref={pdfstartview={XYZ null null 8.00}},aspectratio=169]{beamer}
\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
%\AtBeginDvi{\special{pdf:tounicode EUC-UCS2}}
% テーマ
\usetheme{Copenhagen}
% navi. symbolsは目立たないが，dvipdfmxを使うと機能しないので非表示に
\setbeamertemplate{navigation symbols}{} 
\usepackage{bxdpx-beamer,pxjahyper,minijs}
%\usepackage{graphicx}
%\usepackage{tkokugo,furikana,tsayusen,shiika,sfkanbun,jdkintou,plext}
\usepackage{type1cm}
\usepackage[deluxe]{otf}
%\usepackage{tikzsymbols}
%\usepackage[dvipdfmx]{graphicx}%
\def\pgfsysdriver{pgfsys-dvipdfmx.def}%（graphicxパッケージを使用しない場合はこの行を有効に）
%\def\pgfsysdriver{pgfsys-dvips.def}%デフォルト
%\usepackage[e]{esvect}
\usepackage{tikz}%（これで、pgfとpgfforが読み込まれます。）
%\usepackage{tikz-3dplot}
\usetikzlibrary{calc,intersections,arrows.meta}
%\usetikzlibrary{patterns,angles,backgrounds}
%\usepackage{animate}
%\usepackage{pgfplots}
%\pgfplotsset{compat=newest}
%\pgfplotsset{compat=newest, every axis/.append style={line width=1pt}}
%\PassOptionsToPackage{dvipdfmx}{graphicx}
\nofiles

\hypersetup{% Jul 18 2023
	pdftitle={プレ高数学科（LaTeX Beamer で汎用PDFプレゼンを作る）},
	pdfauthor={gbb60166@gmail.com},
	pdfsubject={https://unilab.gbb60166.jp/prekou/prekou.htm}
	}

% フォントはお好みで
%\usepackage{txfonts}

\mathversion{bold}
\renewcommand{\familydefault}{\sfdefault}
\renewcommand{\seriesdefault}{bx}
\renewcommand{\kanjifamilydefault}{\gtdefault}
\renewcommand{\kanjiseriesdefault}{bx}
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\setbeamerfont{frametitle}{size=\normalsize,series=\bfseries}
\setbeamertemplate{frametitle}[default][center]
\usefonttheme{professionalfonts}

% 参考にしたURL
% http://windom.phys.hirosaki-u.ac.jp/fswiki/wiki.cgi?page=LaTeX+Beamer%A4%C7%A5%D7%A5%EC%A5%BC%A5%F3%A5%C6%A1%BC%A5%B7%A5%E7%A5%F3

\newcommand{\Slash}[1]{\ooalign{\hfil\kern-3pt／\hfil\crcr$#1$}}
\everymath{\displaystyle}

\newcommand{\maruwaku}[1]{\begin{tikzpicture}[scale=0.7, baseline={([yshift=-22pt] current bounding box.north)}]
\filldraw[color=CUDBlue, line width=1pt, rounded corners=2pt] (-0.1,0)--(2.1,0)--(2.1,1.1)--(-0.1,1.1)--cycle;
\draw(1,0.5) node[white]{#1};
\end{tikzpicture}
}

\setbeamersize{text margin left=5mm,text margin right=5mm}
\fboxrule=0.8pt

\makeatletter
\newcommand{\hooklen}[2]{\settowidth{\@tempdima}{\(#1\)}
%\advance\@tempdima by.3ex
% ↑ 数式モードで式の前後に入るスペースを制御したかったが、
%    難しいのでやめた。段々難解なコードになっているのでやめた方がよい？
\hbox to\@tempdima{\hfil \(#2\)\hfil}}
%■等号付き不等号 by 美文書作成入門
\newcommand{\myleqq}{\mathrel{\mathpalette\gl@align<}}
\newcommand{\mygeqq}{\mathrel{\mathpalette\gl@align>}}
\newcommand{\gl@align}[2]{\lower.6ex\vbox{\baselineskip\z@skip\lineskip\z@
	\ialign{$\m@th#1\hfil##\hfil$\crcr#2\crcr=\crcr}}}
\makeatother

% カラーユニバーサルデザインを調べたつもりだがあまり自信がありません
% http://www.fukushihoken.metro.tokyo.jp/kiban/machizukuri/kanren/color.files/colorudguideline.pdf
% http://jfly.iam.u-tokyo.ac.jp/colorset/

% ■ アクセントカラー小面積を目立たせる高彩度色
\definecolor{CUDRed}{RGB}{255,75,0}
\definecolor{CUDGreen}{RGB}{3,175,122}
\definecolor{CUDBlue}{RGB}{0,90,255}
\definecolor{CUDCyan}{RGB}{77,196,255}
\definecolor{CUDMagenta}{RGB}{153,0,153}
\definecolor{CUDYellow}{RGB}{255,241,0}
\definecolor{CUDBrown}{RGB}{128,64,0}

\definecolor{CUDOrange}{RGB}{246,170,0}

% ■ ベースカラー広い面積の塗り分けに用いる低・中彩度色
\definecolor{CUDPink}{RGB}{255,202,191}
\definecolor{CUDBrightGreen}{RGB}{119,217,168}
\definecolor{CUDLime}{RGB}{216,242,85}
\definecolor{CUDCream}{RGB}{255,255,128}
\definecolor{CUDBrightCyan}{RGB}{191,228,255}
%\definecolor{CUD}{RGB}{}%

\setbeamercolor{CUDBrightGreen}{fg=black,bg=CUDBrightGreen!50}
\setbeamercolor{CUDBrightCyan}{fg=black,bg=CUDBrightCyan}
\setbeamercolor{CUDCream}{fg=black,bg=CUDCream!75}

%\setbeamercolor{frametitle}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{palette primary}{use=structure,fg=white,bg=structure.fg}
%\setbeamercolor{frametitle}{bg=CUDOrange}
%\setbeamercolor{palette primary}{bg=CUDOrange}
%\setbeamercolor{frametitle}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{palette primary}{bg=CUDCyan!25,fg=black}
%\setbeamercolor{frametitle}{bg=CUDCream!75,fg=black!80}
%\setbeamercolor{palette primary}{bg=CUDCream!75,fg=black!80}

\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
	{%\fontsize{20}{20}\selectfont%	\displaystyle
		\frac{\raisebox{-.6ex}{\(#1\)}}{\raisebox{.4ex}{\(#2\)}}}%
	{\textstyle{\frac{#1}{#2}}}%	\textstyle
	{%\fontsize{13}{13}\selectfont%	\scriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
		\frac{\raisebox{0ex}{\(#1\)}}{\raisebox{-.4ex}{\(#2\)}}}%
	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■ 本文と数式モードの間に挿入される空白スペース
%\mathsurround=-1pt
%■ \( \log\log \)でlogとlogの間に挿入される細スペース（省略形は \,）
%\thinmuskip=3mu
%■ \( a+b \)で+の前後に挿入される中スペース（省略形は \>）
\medmuskip=1mu plus 1mu minus 1mu
%■ \( x=5 \)で=の前後に挿入される太スペース（省略形は \;）
%\thickmuskip=5mu plus 5mu
% mu は math units の省略で長さの単位

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



%\end{document}
%■■■■■■■■■■■■■　完成品　■■■■■■■■■■■■■■

\begin{frame}[t]
\frametitle{チェバの定理（例題$1$）}
\begin{tikzpicture}[scale=2.4,line join=round,>=stealth,semithick,
	baseline={( [yshift=-2ex] current bounding box.north)}]
\small
\coordinate(B) at (0,0);
\coordinate(C) at (2.4,0);
\coordinate(A) at (2.1,2);
\coordinate(D) at ($(B)!0.625!(C)$);
\coordinate(E) at ($(C)!0.29!(A)$);
\draw(A)--(D)[name path=line AD];
\draw(B)--(E) [name path=line BE];
\path[name intersections={of=line AD and line BE}];
\coordinate(P) at (intersection-1);
\path(C)--($(C)!2!(P)$)[name path=line CP];
\path(A)--(B)[name path=line AB];
\path[name intersections={of=line CP and line AB}];
\coordinate(F) at (intersection-1);
\draw[ultra thick](B)--(C)--(A)--cycle;
\draw(A)--(D)
	(B)--(E)
	(C)--(F);
\begin{scope}[-{Stealth[length=1em]},,line width=2.4pt]
\visible<2->{\draw[CUDRed](A) to[out=180,in=80] (F);
	\draw[CUDRed](F) to[out=180,in=80] (B);
	\draw[CUDBlue](B) to[out=-40,in=220] (D);
	\draw[CUDBlue](D) to[out=-40,in=220] (C);
	\draw[CUDGreen](C) to[out=60,in=-45] (E);
	\draw[CUDGreen](E) to[out=60,in=-45] (A);
	}
\end{scope}

\draw($(A)!0.5!(F)$) node[above left]{$3$};
\draw($(F)!0.5!(B)$) node[above left]{$2$};
\draw($(B)!0.5!(D)$) node[below]{$5$};
\draw($(D)!0.5!(C)$) node[below]{$3$};
\draw($(C)!0.5!(E)$) node[right]{$2$};
\draw($(E)!0.5!(A)$) node[right]{$x$};
\end{tikzpicture}
\hfill
\pause
\begin{minipage}[t]{0.5\textwidth}
\( \myfrac{\,\textcolor{CUDRed}{3}\,}{\textcolor{CUDRed}{2}}
	\times\myfrac{\,\textcolor{CUDBlue}{5}\,}{\textcolor{CUDBlue}{3}}
	\times\myfrac{\,\textcolor{CUDGreen}{2}\,}{\textcolor{CUDGreen}{x}}\ = \,1 \)

\vskip3ex
\qquad が成り立つ
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{チェバの定理（例題$1$）}
\vspace*{-5ex}
\begin{eqnarray*}
\myfrac{\,\textcolor{CUDRed}{3}\,}{\textcolor{CUDRed}{2}}
	\times\myfrac{\,\textcolor{CUDBlue}{5}\,}{\textcolor{CUDBlue}{3}}
	\times\myfrac{\,\textcolor{CUDGreen}{2}\,}{\textcolor{CUDGreen}{x}}
		&=& 1 \\[2ex]\pause
\textcolor{CUDRed}{3}\times
	\textcolor{CUDBlue}{5}\times\textcolor{CUDGreen}{2}
	&=& \textcolor{CUDRed}{2}\times
	\textcolor{CUDBlue}{3}\times\textcolor{CUDGreen}{x} \\[1ex]\pause
\hooklen{3\times5\times2}{30}
	&=& \hooklen{2\times3\times x}{6x} \\[1ex]\pause
\text{\□答}\quad 5 &=& x
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{チェバの定理（例題$2$）}
\begin{tikzpicture}[scale=2.4,line join=round,>=stealth,semithick,
	baseline={( [yshift=-2ex] current bounding box.north)}]
\small
\coordinate(B) at (0,0);
\coordinate(C) at (2.2,0);
\coordinate(A) at (1.8,2.2);
\coordinate(D) at ($(B)!0.6!(C)$);
\coordinate(E) at ($(C)!0.5!(A)$);
\draw(A)--(D)[name path=line AD];
\draw(B)--(E) [name path=line BE];
\path[name intersections={of=line AD and line BE}];
\coordinate(P) at (intersection-1);
\path(C)--($(C)!2!(P)$)[name path=line CP];
\path(A)--(B)[name path=line AB];
\path[name intersections={of=line CP and line AB}];
\coordinate(F) at (intersection-1);
\draw[ultra thick](B)--(C)--(A)--cycle;
\draw(A)--(D)
	(B)--(E)
	(C)--(F);
\begin{scope}[-{Stealth[length=1em]},line width=2.4pt]
\visible<2->{\draw[CUDRed](A) to[out=180,in=90] (F);
	\draw[CUDRed](F) to[out=180,in=90] (B);
	\draw[CUDBlue](B) to[out=-40,in=220] (D);
	\draw[CUDBlue](D) to[out=-40,in=220] (C);
	\draw[CUDGreen](C) to[out=60,in=-45] (E);
	\draw[CUDGreen](E) to[out=60,in=-45] (A);
	}
\end{scope}

\draw($(A)!0.5!(F)$) node[above left]{$x$};
\draw($(F)!0.5!(B)$) node[above left]{$2$};
\draw($(B)!0.5!(D)$) node[below]{$3$};
\draw($(D)!0.5!(C)$) node[below]{$2$};
\draw($(C)!0.5!(E)$) node[right]{$1$};
\draw($(E)!0.5!(A)$) node[right]{$1$};
\end{tikzpicture}
\hfill
\pause
\begin{minipage}[t]{0.5\textwidth}
\( \myfrac{\,\textcolor{CUDRed}{x}\,}{\textcolor{CUDRed}{2}}
	\times\myfrac{\,\textcolor{CUDBlue}{3}\,}{\textcolor{CUDBlue}{2}}
	\times\myfrac{\,\textcolor{CUDGreen}{1}\,}{\textcolor{CUDGreen}{1}}\ = \,1 \)

\vskip3ex
\qquad が成り立つ
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{チェバの定理（例題$2$）}
\vspace*{-5ex}
\begin{eqnarray*}
\myfrac{\,\textcolor{CUDRed}{x}\,}{\textcolor{CUDRed}{2}}
	\times\myfrac{\,\textcolor{CUDBlue}{3}\,}{\textcolor{CUDBlue}{2}}
	\times\myfrac{\,\textcolor{CUDGreen}{1}\,}{\textcolor{CUDGreen}{1}} &=& 1 \\[2ex]
\textcolor{CUDRed}{x}\times
	\textcolor{CUDBlue}{3}\times\textcolor{CUDGreen}{1}
	&=& \textcolor{CUDRed}{2}\times
	\textcolor{CUDBlue}{2}\times\textcolor{CUDGreen}{1} \\[1ex]
\hooklen{x\times3\times1}{3x} &=& \hooklen{2\times2\times1}{4} \\[2ex]
x &=& \myfrac{\,4\,}{3}\quad\text{\□答}
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




\end{document}

