%
%	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}
%\usetikzlibrary{arrows.meta,patterns,angles,intersections,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}
\setbeamerfont{title}{size=\normalsize,series=\bfseries}
\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}

%　斜線（１文字を消す）x
\def\sshasen{\kern-1ex\tikz[baseline=2pt]
	\draw[line width=2pt, CUDBlue](0,0.6)--(0.3,0);}

\newcommand{\ittan}{\begin{tikzpicture}[scale=0.7,
	baseline={([yshift=-21pt] current bounding box.north)}]
\filldraw[very thick,draw=CUDBlue,fill=CUDYellow,rounded corners=1pt]
	(0,0)--++(0.8,0)--++(0,0.8)--++(-0.8,0)--cycle;
\draw(0.4,0.4) node[CUDBlue]
	{\fontsize{7pt}{7pt}\selectfont
		\shortstack{一旦\\[-2pt]停止}};
\end{tikzpicture}
}

%■ 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=2mu plus 1mu minus 1mu
\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{等式の証明（パターンその$1$）}
\maruwaku{問題}\ \( \textcolor{CUDRed}{\text{●}}
	=\textcolor{CUDGreen}{\text{▲}} \)を証明しなさい。
\pause

\medskip
\maruwaku{解答}\ 
%\framebox{
\begin{minipage}[t]{0.8\textwidth}
\( \textcolor{CUDRed}{\text{●}}=\quad
	\text{\footnotesize …\ 計算すると\ …}\quad
	=\textcolor{CUDBlue}{\text{★}} \)\ \ittan

%\smallskip
\( \textcolor{CUDGreen}{\text{▲}}
	=\quad\text{\footnotesize …\ 計算すると\ …}\quad
	=\textcolor{CUDBlue}{\text{★}} \)\ \ittan\pause

\bigskip
計算するとどちらも同じ式\textcolor{CUDBlue}{\text{★}}になるので

\vskip-1ex
\centerline{\( \textcolor{CUDRed}{\text{●}}
	=\textcolor{CUDGreen}{\text{▲}} \)が成り立つ。}
\end{minipage}%}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \textcolor{CUDRed}{(x+y)^2+(x-y)^2}
	=\textcolor{CUDGreen}{2 \,(x^2+y^2)} \)を証明せよ}
\pause

\vspace*{-5ex}
\begin{eqnarray*}
\text{左辺} &=& \textcolor{CUDRed}{\hooklen{x^2+2xy+y^2}{(x+y)^2}
	+\hooklen{x^2-2xy+y^2}{(x-y)^2}}\\\pause
&=& x^2+2xy+y^2+x^2-2xy+y^2 \\
&=& \textcolor{CUDBlue}{2x^2+2y^2}\ \ittan\pause\\[1ex]
%
\text{右辺} &=& \textcolor{CUDGreen}{2 \,(x^2+y^2)}
	= \textcolor{CUDBlue}{2x^2+2y^2}\ \ittan\pause
\end{eqnarray*}

よって\( \textcolor{CUDRed}{(x+y)^2+(x-y)^2}
	=\textcolor{CUDGreen}{2 \,(x^2+y^2)} \)が成り立つ。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{等式の証明（パターンその$2$）}
\maruwaku{問題}\ \( \textcolor{CUDOrange}{\text{■}} \)のとき
\( \textcolor{CUDRed}{\text{●}}
	=\textcolor{CUDGreen}{\text{▲}} \)を証明しなさい。
\pause

\bigskip
\maruwaku{解答}\ 
\begin{minipage}[t]{0.8\textwidth}
\textcolor{CUDOrange}{■}を\textcolor{CUDRed}{●}に代入すると
	\textcolor{CUDBlue}{★}になる。\ittan

\textcolor{CUDOrange}{■}を\textcolor{CUDGreen}{▲}に代入すると
	\textcolor{CUDBlue}{★}になる。\ittan

\bigskip
どちらも同じ式\textcolor{CUDBlue}{★}になるので

\bigskip
\centerline{\( \textcolor{CUDRed}{\text{●}}
	=\textcolor{CUDGreen}{\text{▲}} \)が成り立つ。}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small\( \textcolor{CUDOrange}{a-b=-2} \)のとき
\( \textcolor{CUDRed}{a^2+3b}
	=\textcolor{CUDGreen}{b^2-a+2} \)を証明せよ}
\pause
\quad
\textcolor{CUDOrange}{\( a \quad =b-2 \)}となるので左辺に代入すると

\vspace*{-3ex}
\begin{eqnarray*}
\text{左辺} &=& \textcolor{CUDRed}{\hooklen{b^2-4b+4}{a^2}+3b} \\[1ex]
	&=&
	\textcolor{CUDRed}{\hooklen{b^2-4b+4}{
		\textcolor{CUDOrange}{(b-2)}^2}+3b}\\[1ex]
&=& b^2-4b+4+3b \\[1ex]
&=& b^2-b+4 \quad\ittan
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small\( \textcolor{CUDOrange}{a-b=-2} \)のとき
\( \textcolor{CUDRed}{a^2+3b}
	=\textcolor{CUDGreen}{b^2-a+2} \)を証明せよ}
%\pause
次に\textcolor{CUDOrange}{\( a \ =b-2 \)}を右辺に代入すると

\vspace*{-3ex}
\begin{eqnarray*}
\text{右辺} &=& \textcolor{CUDGreen}{b^2-\hooklen{(b-2)}{a}+2} \\[1ex]
	&=& \textcolor{CUDGreen}{b^2-\textcolor{CUDOrange}{(b-2)}+2} \\[1ex]
&=&  b^2 \hooklen{{}-(b-2)}{-b+2}+2 \\[1ex]
&=&  b^2-b+4 \quad\ittan
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small\( \textcolor{CUDOrange}{a-b=-2} \)のとき
\( \textcolor{CUDRed}{a^2+3b}
	=\textcolor{CUDGreen}{b^2-a+2} \)を証明せよ}
代入して計算すると左辺も右辺も同じ式\( b^2-b+4 \)になるので

\vskip3ex
\centerline{\( \textcolor{CUDRed}{a^2+3b}
	=\textcolor{CUDGreen}{b^2-a+2} \)\qquad
	が成り立つ。}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \textcolor{CUDOrange}{\tfrac{\,a\,}{b}=\tfrac{\,c\,}{d}} \)の
	とき\( \textcolor{CUDRed}{\tfrac{b}{\,a+b\,}}
	=\textcolor{CUDGreen}{\tfrac{d}{\,c+d\,}} \)
	%見えない支柱を入れる
	\rule[-14pt]{0pt}{3pt}
	を証明せよ}
\pause
\textcolor{CUDOrange}{\( \myfrac{\,a\,}{b}=\myfrac{\,c\,}{d} \)}
	\( {}=k \)\quad とおくと

\vskip-2ex
\begin{eqnarray*}
\only<2>{\textcolor{CUDOrange}{\myfrac{\,a\,}{b}} &=& k \\[1ex]
	\textcolor{CUDBlue}{b\times}\textcolor{CUDOrange}{\myfrac{\,a\,}{b}}
		&=& k\textcolor{CUDBlue}{\times b} \\[1ex]
	\textcolor{CUDOrange}{a} &=& k \textcolor{CUDBlue}{b}
	}
\only<3>{\textcolor{CUDOrange}{\myfrac{\,c\,}{d}} &=& k \\[1ex]
	\textcolor{CUDBlue}{d\times}\textcolor{CUDOrange}{\myfrac{\,c\,}{d}}
		&=& k\textcolor{CUDBlue}{\times d} \\[1ex]
	\textcolor{CUDOrange}{c} &=& k \textcolor{CUDBlue}{d}
	}
	\quad\ittan
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \textcolor{CUDOrange}{\tfrac{\,a\,}{b}=\tfrac{\,c\,}{d}} \)の
とき\( \textcolor{CUDRed}{\tfrac{b}{\,a+b\,}}
	=\textcolor{CUDGreen}{\tfrac{d}{\,c+d\,}} \)
	%見えない支柱を入れる
	\rule[-14pt]{0pt}{3pt}
	を証明せよ}
%\pause
\quad
\colorbox{CUDCream}{\( a=kb \)}\ を左辺に代入すると

\bigskip
\( \textcolor{CUDRed}{\myfrac{b}{\colorbox{CUDCream}{$a$}+b\,}}
	=\myfrac{b}{\colorbox{CUDCream}{\(kb\)}+b\,}
	= \myfrac{b\sshasen}{\,b\sshasen\,(k+1)\,}
	= \myfrac{1}{\ k+1 \ } \ \ittan \)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \textcolor{CUDOrange}{\tfrac{\,a\,}{b}=\tfrac{\,c\,}{d}} \)の
	とき\( \textcolor{CUDRed}{\tfrac{b}{\,a+b\,}}
	=\textcolor{CUDGreen}{\tfrac{d}{\,c+d\,}} \)
	%見えない支柱を入れる
	\rule[-14pt]{0pt}{3pt}
	を証明せよ}
%\pause
\quad
\colorbox{CUDCream}{\( c=kd \)}\ を右辺に代入すると

\bigskip
\( \textcolor{CUDRed}{\myfrac{d}{\colorbox{CUDCream}{$c$}+d\,}} 
	= \myfrac{d}{\colorbox{CUDCream}{\(kd\)}+d\,}
	=\myfrac{d\sshasen}{\,d\sshasen\,(k+1)\,}
	=\myfrac{1}{\ k+1 \ } \ \ittan \)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\( \textcolor{CUDOrange}{\tfrac{\,a\,}{b}=\tfrac{\,c\,}{d}} \)の
	とき\( \textcolor{CUDRed}{\tfrac{b}{\,a+b\,}}
	=\textcolor{CUDGreen}{\tfrac{d}{\,c+d\,}} \)
	%見えない支柱を入れる
	\rule[-14pt]{0pt}{3pt}
	を証明せよ}
代入して計算すると左辺も右辺も同じ式\( \myfrac{1}{\ k+1 \ } \)になるので

\vskip3ex
\centerline{\( \textcolor{CUDRed}{\myfrac{b}{\,a+b\,}}
	=\textcolor{CUDGreen}{\myfrac{d}{\,c+d\,}} \)\quad が成り立つ。
	}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}

