%
%	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}
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\documentclass[20pt,dvipdfmx,usepdftitle=false,aspectratio=169]{beamer}
% pdfの栞の字化けを防ぐ
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% 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}
%\usetikzlibrary{arrows.meta,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
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% 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

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\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};
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\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
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% 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
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\definecolor{CUDGreen}{RGB}{3,175,122}
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\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
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\definecolor{CUDBrightGreen}{RGB}{119,217,168}
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\newcommand{\myfrac}[2]{\mathchoice%■ 修正 Oct 8,2023
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	{\textstyle{\frac{#1}{#2}}}%	\textstyle
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	{%\fontsize{11}{11}\selectfont%	\scriptscriptstyle
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	}


\begin{document}

\title{プレ高数学科}\author{gbb60166}

\newcommand{\katamuitachokkaku}[4]{%■傾いた直角記号の\newcommandを定義
\draw($ (#1)!#4!(#2) $)% #1から#2方向へ、長さ#4進んだ点（ココをXとする）
	--($ (#1)!#4!(#2)+(#1)!#4!(#3)-(#1) $)
% Xに、ベクトル【(#1)!#4!(#3) - (#1)】を加えた点
% Xに、ベクトル【先端 - 根本】を加えた点
% Xに、ベクトル【#1から#3方向へ、長さ#4進んだ地点 - 点#1】を加えた点
	--($ (#1)!#4!(#3) $);% #1から#3方向へ、長さ#4進んだ点
	}
\newcommand{\defcoor}{\coordinate(A) at ({sqrt(2)},1);
%たけしの解答　とは別に作ったのでABCDの付け方が違っています
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	%■結果論となるが、これでもよい
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	%\coordinate(C') at ($ (B)!1/3!(C) $);
	\coordinate(A') at ($ (P)+(P)-(A) $);
	}

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■



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

\begin{frame}[t]
\frametitle{問題}
長方形の紙（\(\textrm{A}4\)判）を数学的に三等分せよ

\quad ※\ 横置きの場合\quad\( \mbox{縦}:\mbox{横}=1:\sqrt{2} \)
\vskip2ex
\small
\centerline{たけしのコマ大数学科 DVDBOX}

\centerline{６限目、問\ajMaru{28}、三つ折り}

\vskip4ex
※\ 
\begin{minipage}[t]{0.9\textwidth}
折り目を付けて、正確に三等分に折ってください
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{解答}
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	baseline={([yshift=-2ex] current bounding box.north)}]
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\scriptsize
\defcoor

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%■デバッグ用
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%	\draw(\z) node{\fontsize{6}{6}\selectfont\textrm{\z}};
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{解説\quad 相似の三角形に注目します}
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	baseline={([yshift=-2ex] current bounding box.north)}]
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		(C) node[right]{\textrm{C}}
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		(D) to node[fill=white]{\(\sqrt{2}\)} (C)
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\small
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		&=& 2 : 1 \\
	\end{eqnarray*}
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\visible<4>{\draw(1.8,-1.5)
	node{縦横比\ \( 1:\sqrt{2} \)\ のときしか使えません};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(1\)}
\begin{tikzpicture}[scale=2.4,semithick, >=stealth,line join=round,
%	gbb/.style={fill=white,inner sep=2pt},
	baseline={([yshift=-2ex] current bounding box.north)}]
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\useasboundingbox(-3,-1) grid (3,1);
\scriptsize
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\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(2\)}
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\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(3\)}
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\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(4\)}
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\visible<7,9>{\draw[dashed](D)--(F);
	}
\visible<8>{\filldraw[fill=CUDBrightCyan]
		(A)--(B)--(D)--(H)--cycle;
		\draw[dashed](O)--(E)
			(O)--(G)
			(D)--($ (H)!0.5!(O) $);
	\filldraw[fill=CUDCream]
		($ (A)!(C)!(H)!-1!(C) $)--(A)--(H)--cycle;
	\draw[dashed]
		($ (A)!0.5!(H) $)--($ (A)!(C)!(H)!-1!(C)!0.5!(H) $)
			--($ (H)!1/3!(A) $);
	}
\visible<9>{\draw[dashed](H)--(A);
	\color{CUDRed}
	\draw($ (B)!1/3!(A) $)--($ (D)!1/3!(C) $)
		($ (B)!2/3!(A) $)--($ (D)!2/3!(C) $);
	\fill($ (D)!2/3!(F) $) circle(0.8pt);
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(5\)}
\begin{tikzpicture}[scale=2.4,semithick, >=stealth,line join=round,
%	gbb/.style={fill=white,inner sep=2pt},
	baseline={([yshift=-2ex] current bounding box.north)}]
%\draw[help lines](-7.5,-3.5) grid (7.5,3.5);
\useasboundingbox(-3,-1) grid (3,1);
\scriptsize
\defcoor

\coordinate(E) at ($ (B)!0.5!(D) $);
\coordinate(F) at ($ (A)!0.5!(C) $);
\coordinate(G) at ($ (A)!0.5!(B) $);
\coordinate(H) at ($ (D)!0.5!(C) $);

\visible<1,3,5,7>{\filldraw[fill=CUDBrightCyan]
			(A)--(B)--(D)--(C)--cycle;
	}
\visible<2>{\filldraw[fill=CUDCream](B)--(E)--(F)--(A)--cycle;
	}
\visible<3,5,7>{\draw[dashed](O)--(E)
			(O)--(F);
	}
\visible<4>{\filldraw[fill=CUDBrightCyan](E)--(D)--(C)--(A)--cycle;
	\draw[dashed](O)--(F);
	\filldraw[fill=CUDCream]
		($ (E)!(B)!(A)!-1!(B) $)--(A)--(E)--cycle;
	}
\visible<5,7>{\draw[dashed](E)--(A);
	}
\visible<6>{\filldraw[fill=CUDBrightCyan](B)--(D)--(C)--cycle;
	\draw[dashed](O)--(E)
		(E)--($ (O)!0.5!(G)!0.5!(E) $);
	\filldraw[fill=CUDCream]
		($ (B)!(A)!(C)!-1!(A) $)--(B)--(C)--cycle;
	\draw[dashed]($ (B)!(A)!(C)!-1!(A) $)--($ (B)!1/3!(C) $);
	}
\visible<7>{\draw[dashed](B)--(C);
	\color{CUDRed}
	\draw($ (B)!1/3!(A) $)--($ (D)!1/3!(C) $)
		($ (B)!2/3!(A) $)--($ (D)!2/3!(C) $);
	\fill($ (B)!1/3!(C) $) circle(0.8pt);
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{三つ折り\quad 別解\(6\)}
\begin{tikzpicture}[scale=2.4,semithick, >=stealth,line join=round,
%	gbb/.style={fill=white,inner sep=2pt},
	baseline={([yshift=-2ex] current bounding box.north)}]
%\draw[help lines](-7.5,-3.5) grid (7.5,3.5);
\useasboundingbox(-3,-1) grid (3,1);
\scriptsize
\defcoor

\coordinate(E) at ($ (B)!0.5!(D) $);
\coordinate(F) at ($ (A)!0.5!(C) $);
\coordinate(G) at ($ (A)!0.5!(B) $);
\coordinate(H) at ($ (D)!0.5!(C) $);

\visible<1,3,5,7>{\filldraw[fill=CUDBrightCyan]
			(A)--(B)--(D)--(C)--cycle;
	}
\visible<2>{\filldraw[fill=CUDCream](B)--(D)--(H)--(G)--cycle;
	}
\visible<3,5,7>{\draw[dashed](O)--(G)
			(O)--(H);
	}
\visible<4>{\filldraw[fill=CUDBrightCyan](B)--(D)--(C)--(G)--cycle;
	\draw[dashed](O)--(H);
	\filldraw[fill=CUDCream]
		($ (G)!(A)!(C)!-1!(A) $)--(G)--(C)--cycle;
	}
\visible<5,7>{\draw[dashed](G)--(C);
	}
\visible<6>{\filldraw[fill=CUDBrightCyan](A)--(D)--(B)--cycle;
	%\draw[dashed](O)--(E)
	%	(E)--($ (O)!0.5!(G)!0.5!(E) $);
	\filldraw[fill=CUDCream]
		($ (A)!(C)!(D)!-1!(C) $)--(A)--(D)--cycle;
	%\draw[dashed]($ (A)!(C)!(D)!-1!(C) $)--($ (B)!1/3!(C) $);
	}
\visible<7>{\draw[dashed](A)--(D);
	\color{CUDRed}
	\draw($ (B)!1/3!(A) $)--($ (D)!1/3!(C) $)
		($ (B)!2/3!(A) $)--($ (D)!2/3!(C) $);
	\fill($ (A)!1/3!(D) $) circle(0.8pt);
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{番外編\quad 五つ折り}
\begin{tikzpicture}[scale=2.4,semithick, >=stealth,line join=round,
%	gbb/.style={fill=white,inner sep=2pt},
	baseline={([yshift=-2ex] current bounding box.north)}]
%\draw[help lines](-7.5,-3.5) grid (7.5,3.5);
\useasboundingbox(-3,-1) grid (3,1);
\scriptsize
\defcoor

\coordinate(E) at ($ (B)!0.5!(D) $);
\coordinate(F) at ($ (A)!0.5!(C) $);
\coordinate(G) at ($ (A)!0.5!(B) $);
\coordinate(H) at ($ (D)!0.5!(C) $);

\visible<1,4,6,8->{\filldraw[fill=CUDBrightCyan]
			(A)--(B)--(D)--(C)--cycle;
	}
\visible<2>{\filldraw[fill=CUDCream](B)--(D)--(H)--(G)--cycle;
	}
\visible<3>{\filldraw[fill=CUDCream]
		(B)--(D)--($ (D)!0.5!(H) $)--($ (B)!0.5!(G) $)--cycle;
	}
\visible<4,6,8->{\draw[dashed](G)--(H)
			($ (B)!0.5!(G) $)--($ (D)!0.5!(H) $)
			($ (G)!0.5!(A) $)--($ (H)!0.5!(C) $);
	}
\visible<5>{\filldraw[fill=CUDBrightCyan](B)--(D)--(A)--cycle;
	\filldraw[fill=CUDCream]
		($ (D)!(C)!(A)!-1!(C) $)--(D)--(A)--cycle;
	\draw[dashed]($ (D)!(C)!(A)!-1!(C)!0.25!(D) $)--($ (A)!0.25!(D) $)
		($ (D)!(C)!(A)!-1!(C)!0.5!(D) $)--($ (A)!0.5!(D) $)
		($ (D)!(C)!(A)!-1!(C)!0.75!(D) $)--($ (A)!0.75!(D) $);
	}
\visible<6,8->{\draw[dashed](A)--(D);
	}
\visible<7>{\filldraw[fill=CUDBrightCyan]
		(C)--($ (A)!0.5!(G) $)--(B)--(D)--cycle;
		\draw[dashed](G)--(H)
			($ (B)!0.5!(G) $)--($ (D)!0.5!(H) $)
			($ (G)!0.5!(A) $)--($ (H)!0.5!(C) $)
			(D)--($ (D)!0.75!(A) $);
	\filldraw[fill=CUDCream]
		($ (A)!0.5!(G)!(A)!(C)!-1!(A) $)--(C)
			--($ (A)!0.5!(G) $)--cycle;
	\draw[dashed]($ (A)!0.5!(G)!(A)!(C)!-1!(A) $)
			--($ (G)!0.5!(A)!0.2!(C) $);
	}
\visible<8->{\draw[dashed]($ (G)!0.5!(A) $)--(C);
	\color{CUDRed}
	\draw($ (B)!0.2!(A) $)--($ (D)!0.2!(C) $)
		($ (B)!0.4!(A) $)--($ (D)!0.4!(C) $)
		($ (B)!0.6!(A) $)--($ (D)!0.6!(C) $)
		($ (B)!0.8!(A) $)--($ (D)!0.8!(C) $);
	\fill($ (A)!1/5!(D) $) circle(0.8pt);
	}

\normalsize
\visible<9>{\draw($ (D)!0.5!(C) $)++(0,-1ex)
	node{奇数等分は無限に折ることができるそうです};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%\begin{frame}[t]
%\frametitle{たけしの解答}
%\begin{tikzpicture}[scale=2.4,semithick, >=stealth,line join=round,
%	baseline={([yshift=-2ex] current bounding box.north)}]
%%\draw[help lines](-7.5,-3.5) grid (7.5,3.5);
%\useasboundingbox(-3,-1) grid (3,1);
%\scriptsize
%\coordinate(A) at ({-sqrt(2)},1);
%\coordinate(B) at ({-sqrt(2)},-1);
%\coordinate(C) at ({sqrt(2)},-1);
%\coordinate(D) at ({sqrt(2)},1);
%
%\coordinate(I) at ($ (A)!0.5!(B) $);
%\coordinate(J) at ($ (B)!0.5!(C) $);
%\coordinate(K) at ($ (C)!0.5!(D) $);
%\coordinate(L) at ($ (A)!0.5!(D) $);
%
%\coordinate(O) at ($ (I)!0.5!(K) $);
%
%\coordinate(S) at ({-sqrt(2)/3},1/3);
%\coordinate(T) at ({-sqrt(2)/3},-1/3);
%\coordinate(U) at ({sqrt(2)/3},-1/3);
%\coordinate(V) at ({sqrt(2)/3},1/3);
%
%\coordinate(AtoID) at ($ (I)!(A)!(D) $);
%\coordinate(A') at ($ (AtoID)+(AtoID)-(A) $);
%
%\coordinate(AtoBL) at ($ (B)!(A)!(L) $);
%\coordinate(A'') at ($ (AtoBL)+(AtoBL)-(A) $);
%
%
%\visible<1,3,5,7,9,12>{\filldraw[fill=CUDBrightCyan]
%			(A)--(B)--(C)--(D)--cycle;
%	}
%\visible<2>{\filldraw[fill=CUDCream](A)--(I)--(K)--(D)--cycle;}
%\visible<3>{\draw[dashed](I)--(O)
%			(K)--(O);
%	}
%\visible<4>{\filldraw[fill=CUDCream](A)--(B)--(J)--(L)--cycle;
%	\draw[dashed](I)--(O);
%	}
%\visible<5>{\draw[dashed](I)--(O)
%			(J)--(O)
%			(K)--(O)
%			(L)--(O);
%	}
%\visible<6>{\filldraw[fill=CUDBrightCyan](I)--(B)--(C)--(D)--cycle;
%		\draw[dashed]%(I)--(O)
%				(J)--(O)
%				(K)--(O);
%	\filldraw[fill=CUDCream](A')--(I)--(D)--cycle;
%		\draw[dashed]($ (L)!0.5!(O) $)--($ (A')!0.5!(D) $);
%	}
%\visible<7>{\draw[dashed](I)--(O)
%			(J)--(O)
%			(K)--(O)
%			(L)--(O)
%			(D)--($ (O)!0.5!(L) $)
%			(I)--($ (O)!0.5!(L) $);
%	}
%\visible<8>{\filldraw[fill=CUDBrightCyan](B)--(C)--(D)--(L)--cycle;
%	\draw[dashed](D)--($ (O)!0.5!(L) $)
%			(J)--(O)
%			(K)--(O);
%	\filldraw[fill=CUDCream](A'')--(B)--(L)--cycle;
%	\draw[dashed]($ (O)!0.5!(I) $)--($ (A'')!0.5!(B) $)--(S);
%	}
%\visible<9>{\draw[dashed](I)--(O)
%			(K)--(O)
%			(J)--(O)
%			(L)--(O)
%			(D)--($ (O)!0.5!(L) $)
%			(I)--($ (O)!0.5!(L) $)
%			(B)--(L);
%		\fill[CUDRed](S) circle(0.8pt);
%	}
%\visible<10>{\filldraw[fill=CUDBrightCyan]
%			(L)--(J)--(B)--(A)--cycle;
%	\draw[dashed](I)--($ (O)!0.5!(L) $)
%			(I)--(O)
%			(B)--(L);
%	\filldraw[fill=CUDCream]
%		($ (A)!(S)!(D) $)--($ (B)!(S)!(C) $)
%		--($ (B)!(V)!(C) $)--($ (A)!(V)!(D) $)--cycle;
%	\draw[dashed]($ (A)!1/3!(D) $)--($ (D)!1/3!(I) $)
%			($ (I)!1/3!(K) $)--($ (I)!2/3!(K) $);
%	\fill[CUDRed](S) circle(0.8pt);
%	}
%\visible<11>{\filldraw[fill=CUDCream]
%		($ (A)!(S)!(D) $)--($ (B)!(S)!(C) $)
%		--($ (B)!(V)!(C) $)--($ (A)!(V)!(D) $)--cycle;
%	\draw[dashed]($ (I)!1/3!(K) $)--($ (I)!2/3!(K) $)
%			($ (I)!2/3!(K) $)--($ (I)!1/3!(D) $)
%				--($ (B)!2/3!(C) $);
%	\fill[CUDRed](S) circle(0.8pt);
%	}
%\visible<12>{\draw[dashed](I)--(O)
%			(K)--(O)
%			(J)--(O)
%			(L)--(O)
%			(D)--($ (O)!0.5!(L) $)
%			(I)--($ (O)!0.5!(L) $)
%			(B)--(L);
%		\draw[CUDRed]($ (A)!(S)!(D) $)--($ (B)!(S)!(C) $)
%			($ (B)!(V)!(C) $)--($ (A)!(V)!(D) $);
%	\fill[CUDRed](S) circle(0.8pt);
%	}
%
%%■デバッグ用
%%\foreach \z in {A,B,C,D,I,J,K,L,S,T,U,V}
%%	\draw(\z) node{\fontsize{6}{6}\selectfont\textrm{\z}};
%\end{tikzpicture}
%\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}

