%
%	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）
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\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
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\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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% ↑ 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？
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%■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{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}
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\begin{document}

\title{プレ高数学科}\author{gbb60166}

\newcommand{\defABC}{\coordinate[label=left:{\tiny A}] (A) at (0,0);
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	\draw[<->](20,#1)-- node[gbb]{$6$}(26,#1);
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%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■


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

\begin{frame}[t]
\frametitle{\alt<2->{解説}{問題}}
\hspace*{-3ex}
\begin{tikzpicture}[scale=0.2,>=stealth,
	gbb/.style={inner sep=2pt, fill=white},
	baseline=(current bounding box.north)]
\defABC
\coordinate[label=right:{\tiny D}] (D) at (2,-6);

\defSTU
\defGEF
% ----------------------
\defdash

\draw[very thick](D)--(C)--(B)--(A)--(S)--(T)--(U)--(G)--(F)--(E)
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	\draw(15,-9) node[inner sep=0pt,fill=white,text width=4em]
		{\small DEは半円単位は \( (\mathrm{m}) \)};
	}

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			(0,-2)--(1,-1)--(2,-2)--(1,-3)--cycle
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	(-4,-2)--(B)
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	(-4,-6)--(D);

\foreach \y in {0,-2,-4}\draw[<->](-3,\y)--++(0,-2)
	node[midway,xshift=-1ex,inner sep=0pt,fill=white]{\tiny $2$};
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	(4,7)--(S)
	(10,7)--(T)
	(16,7)--(U)
	(20,7)--(G)
	(26,7)--(F);
\tiny
\foursix{6.5}

\scriptsize
\draw[semithick,line join=round](0,-20) node[below]{南}
		--++(0,4) node[above]{北}--++(-0.5,-1.2)--++(1,0)
	(-1,-18.5)--++(2,0);
\end{tikzpicture}
\hfill
\begin{minipage}[t]{0.5\textwidth}
\only<1>{図のような、周りを同じ高さの塀で囲まれた土地がある。
	ここに太陽が真南から照り付け、影の長さが$2$ \textrm{m}に
	なったときの影の面積は？\\[1ex]

	\footnotesize
	\centerline{たけしのコマ大数学科 DVDBOX 第$2$期}
	\centerline{４時限、問\ajMaru{16}、影より}
	}
\only<2-3>{影は左図のようになります。}

\only<3>{\bigskip
	長方形、平行四辺形、半円などに分けて面積を
	求める方法もありますが、\textcolor{CUDRed}{積分}の
	考え方を使うと簡単に求められます。
	}
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{積分の考え方}
\begin{tikzpicture}[scale=0.4, >=stealth,
	gbb/.style={inner sep=2pt, fill=white}]
\coordinate[label=below:{\footnotesize A}] (A) at (0,0);

\defSTU
\coordinate[label=below:{\footnotesize G}] (G) at (20,0);
\coordinate[label=below:{\footnotesize F}] (F) at (26,0);
\defdash

\draw(A)--++(0,7)
	(S)--++(0,3)
	(T)--++(0,9)
	(U)--++(0,3)
	(G)--++(0,7)
	(F)--++(0,7);

\foursix{6.5}

\fill[CUDRed, opacity=0.5](A')--(S')--(T')--(U')--(G')--(F')
	--(F)--(G)--(U)--(T)--(S)--(A)--cycle;
\draw(A')--(S')--(T')--(U')--(G')--(F')--(F)--(G)--(U)--(T)--(S)--(A)--cycle;

\draw(F)--++(3,0)
	(F')--++(3,0);
\draw[<->](F)++(2,0)--  node[gbb]{$2$}++(0,2);

\visible<2>{\foreach \s in {0,0.2,...,4}
		\draw[CUDBlue, very thick] (\s,\s)--++(0,2);
	\foreach \s in {4,4.2,...,10}
		\draw[CUDBlue, very thick] (\s,-1*\s+8)--++(0,2);
	\foreach \s in {10,10.2,...,16}
		\draw[CUDBlue, very thick] (\s,\s-12)--++(0,2);
	\foreach \s in {16,16.2,...,20}
		\draw[CUDBlue, very thick] (\s,-1*\s+20)--++(0,2);
	\foreach \s in {20,20.2,...,26}
		\draw[CUDBlue, very thick] (\s,0)--++(0,2);
	}
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		\draw[CUDBlue, very thick] (\s,0)--++(0,2);
	\draw[CUDRed,<->,very thick](0,3)-- node[gbb]{$26$}++(26,0)
		;
	}
\end{tikzpicture}

\vskip3ex
\visible<3>{\centerline{この部分の面積は
	\( 26\times2=52 \:\textrm{m}^2 \)となる}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{積分の考え方}
\vspace*{-1ex}
\begin{tikzpicture}[scale=0.4, >=stealth,
	gbb/.style={inner sep=2pt, fill=white}]
\coordinate(A) at (0,0);
\coordinate(B) at (2,-2);
\coordinate(C) at (0,-4);
\coordinate(D) at (2,-6);

\coordinate(G) at (20,0);
\coordinate(F) at (26,0);

\defSTU
\coordinate(E) at (26,-6);
\defdash

\draw(-4,-2)--(0,-2)
	(-4,-4)--(C);

\draw[<->](-3,-2)-- node[gbb]{$2$}(-3,-4);

\draw(0,-4)--++(0,4)
	(26,-8)--++(0,8);

\foursix{-1.5}

\fill[CUDRed, opacity=0.5](E)
	arc[start angle=0, end angle=-180, radius=12]--(C)--(C')--(D')
	arc [start angle=-180, end angle=0, radius=12]--(E)--cycle;

\visible<2>{\foreach \s in {0,0.2,...,2}
		\draw[CUDBlue, very thick] (\s,-\s-4)--++(0,2);
	\foreach \s in {2,2.2,...,26}
		\draw[CUDBlue, very thick]($ (\s,{-sqrt(12^2-(\s-14)^2)-6}) $)
			--++(0,2);
	}
\visible<3>{\foreach \s in {0,0.2,...,26}
		\draw[CUDBlue, very thick] (\s,-4)--++(0,2);
	\draw[CUDRed,<->,very thick](0,-0.5)-- node[gbb]{$26$}++(26,0);
	\draw(13,-8) node{この部分の面積も\( 26\times2=52 \:\textrm{m}^2 \)と
	なる};
	}
\end{tikzpicture}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{後はこの部分の面積を求めれば良い}
\vspace*{-3ex}
\begin{tikzpicture}[scale=1, >=stealth,
	gbb/.style={inner sep=2pt, fill=white},
	baseline=(current bounding box.north)]
\defABC
\coordinate(O) at (1,1);
\coordinate(P) at (1,-3);
\coordinate(Q) at (1,-1);
%-----------------------------
\coordinate(B') at ($ (B)+(0,2) $);
\coordinate(C') at ($ (C)+(0,2) $);

\fill[CUDRed, opacity=0.5](A)--(O)--(B')--(B)--(P)--(C')--(Q)--cycle;

\draw(O)--(B')--(C')--(P);
\draw[very thick](C)--(B)--(A)--(2,2);

\draw(B')--++(1.2,0)
	(B)--++(1.2,0);

\draw[<->](B)++(0.7,0)-- node[gbb]{\scriptsize $2$}++(0,2);

\color{CUDBlue}
\visible<2->{\scriptsize
	\draw[<->, very thick](O)
		-- node[inner sep=0pt, fill=white]{$\sqrt{2}$}(B');
	\draw[<->, very thick](P)
		-- node[inner sep=0pt, fill=white]{$\sqrt{2}$}(C');
	\footnotesize
	\draw(1,0) node[gbb]{$2$};
	\draw(1,-2) node[gbb]{$2$};
	}
\visible<3->{\draw(1.6,-1) node[gbb]{$1$};}
\end{tikzpicture}
\hfill
\begin{minipage}[t]{0.6\textwidth}
\pause
正方形の一辺は\(\sqrt{2}\)となるので、二つの正方形の面積はそれぞれ$2$となる。
\pause

\bigskip
三角形の面積は、その半分なので$1$となる。
\pause

\bigskip
よって、この部分の面積は$5$となる。
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{問題}
\hspace*{-3ex}
\begin{tikzpicture}[scale=0.2, >=stealth,
	gbb/.style={inner sep=2pt, fill=white},
	baseline=(current bounding box.north)]
\defABC
\coordinate[label=right:{\tiny D}] (D) at (2,-6);

\defSTU
\defGEF
\defdash

\draw[very thick](D)--(C)--(B)--(A)--(S)--(T)--(U)--(G)--(F)--(E)
	arc [start angle=0, end angle=-180, radius=12];

\fill[CUDBlue, opacity=0.5](A)--(1,1)--(B')--(B)
	--(1,-3)--(0,-2)--(1,-1)--cycle;
\fill[CUDGreen, opacity=0.5](E)
	arc[start angle=0, end angle=-180, radius=12]--(C)--(C')--(D')
	arc [start angle=-180, end angle=0, radius=12]--(E)--cycle;

\fill[CUDRed, opacity=0.5](A')--(S')--(T')--(U')--(G')--(F')
	--(F)--(G)--(U)--(T)--(S)--(0,0)--cycle;

\draw(D')--(C')--(B')--(A')--(S')--(T')--(U')--(G')--(F')--(E')
	arc [start angle=0, end angle=-180, radius=12]--cycle;
\draw[very thick](D)--(C)--(B)--(A)--(S)--(T)--(U)--(G)--(F)--(E)
	arc [start angle=0, end angle=-180, radius=12]--cycle;

\draw(-4,0)--(A)
	(-4,-2)--(B)
	(-4,-4)--(C)
	(-4,-6)--(D);

\foreach \y in {0,-2,-4}\draw[<->](-3,\y)--++(0,-2)
	node[midway,xshift=-1ex,inner sep=0pt,fill=white]{\tiny $2$};
\draw(0,7)--(A)
	(4,7)--(S)
	(10,7)--(T)
	(16,7)--(U)
	(20,7)--(G)
	(26,7)--(F);
\tiny
\foursix{6.5}

\scriptsize
\draw[semithick,line join=round](0,-20) node[below]{南}
		--++(0,4) node[above]{北}--++(-0.5,-1.2)--++(1,0)
	(-1,-18.5)--++(2,0);
\end{tikzpicture}
\hfill
\begin{minipage}[t]{0.5\textwidth}
よって影の面積は\pause

\[ \textcolor{CUDRed}{52}+\textcolor{CUDGreen}{52}+\textcolor{CUDBlue}{5}
	=109\,\textrm{m}^2 \ \text{\□答}\]
\end{minipage}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\end{document}
