%
%	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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% pdfの栞の字化けを防ぐ
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% テーマ
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% 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
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\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。）
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%\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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\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

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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？
\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{CUDBlue}{RGB}{0,90,255}
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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}
\definecolor{CUDLime}{RGB}{216,242,85}
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\begin{document}

\title{プレ高数学科}\author{gbb60166}

%■■■■■■■■■■■■■　テスト領域　■■■■■■■■■■■■■■


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

\begin{frame}[t]
\frametitle{\small コマ大数学科 DVD BOX$1$、$1$限目、問\ajMaru{5}ケプラー予想}
\begin{tikzpicture}[scale=0.2, thick, >=stealth,
	gbb/.style={fill=white,inner sep=1pt}]
\fill[CUDCream](0,0) rectangle (62.5,10);

\draw(25,0)--(0,0)--(0,10)--(25,10)
	(35,0)--(62.5,0)--(62.5,10)--(35,10);
\footnotesize
\draw[<->](0,12)-- node[gbb]{\( 502.5 \textrm{cm} \)}(62.5,12);
\draw[<->](-2,0)-- node[gbb,rotate=90]{\( 10 \textrm{cm} \)}(-2,10) ;
\draw(30,5) node{\large\(\cdots\)};
\visible<2->{\foreach \y in {2.5,7.5}
	\foreach \x in {0,1,2,3,8,9,10,11}
		\filldraw[fill=CUDBrightCyan,draw=black]
			(5*\x+2.5,\y) circle (2.5);
	}
\end{tikzpicture}

\vspace*{2ex}
\only<1>{上のような長方形の中に、直径\(5\ \textrm{cm}\)の円を
	いくつ入れることができる？}
\only<2>{上のような入れ方だと$200$個しか入らない。}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small コマ大数学科 DVD BOX$1$、$1$限目、問\ajMaru{5}ケプラー予想}
\begin{tikzpicture}[scale=0.45, thick, >=stealth,
	gbb/.style={fill=white,inner sep=1pt}]
\coordinate [label=left:{\tiny A}] (A) at (2.5,2.5);
\coordinate [label=below:{\tiny B}] (B) at (7.5,2.5);
\coordinate [label=left:{\tiny C}] (C) at ($ (5,{2.5*sqrt(3)+2.5}) $);
\coordinate [label=below:{\tiny D}]
	(D) at ($ ({5+sqrt(5^2-(5-2.5*sqrt(3))^2)},7.5) $);
\coordinate [label=above:{\tiny E}] (E) at ($ (D)+(5,0) $);
\coordinate [label=below:{\tiny F}] (F) at ($ (D)+(2.5,{-2.5*sqrt(3)}) $);
\coordinate [label=below:{\tiny G}]
	(G) at ($ (A)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate [label=below:{\tiny H}]
	(H) at ($ (B)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate [label=right:{\tiny I}]
	(I) at ($ (C)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate(X) at (5,7.5);

%\fill[CUDCream](0,0) rectangle (25,10);
\draw(24,0)--(0,0)--(0,10)--(24,10);
\foreach \a in {A,...,I}{\fill(\a) circle(3pt);
%	\filldraw[fill=white,draw=black](\a) circle (2.5);
	\draw(\a) circle (2.5);
	}
\draw[CUDBlue](A)--(B)--(C)--cycle
	(D)--(E)--(F)--cycle
	(G)--(H)--(I)--cycle;

\visible<2->{\fill (X) circle (3pt);
	\draw(X) node[left,yshift=3pt]{\tiny X};
	\draw[CUDGreen](C)--(X)--(D)--cycle
		(X) rectangle ++(9pt,-9pt);
	}
\visible<3->{\draw[CUDRed, dashed] (C) to[out=-25,in=220]
		node[inner sep=1pt, fill=white]{\scriptsize $5$} (D);
	\draw[CUDRed, <->](A)-- node[gbb,rotate=90]{\scriptsize $2.5$}
					++(0,-2.5);
	\draw[CUDRed, <->](D)-- node[gbb,rotate=90]{\scriptsize $2.5$}
					++(0,2.5);
	\draw[CUDRed, <->](X)-- node[gbb,rotate=90]{\scriptsize $2.5$}
					++(0,2.5);
	}
\visible<4->{\draw[CUDRed, <->](A)++(2.5,0)
	-- node[gbb,rotate=90]{\tiny$2.5\sqrt{3}$}(C);
	\draw[CUDRed](A)++(16pt,0)
		arc[start angle=0, end angle=60,radius=16pt];
	\draw[CUDRed](A)++(20pt,16pt) node[right, inner sep=0pt, fill=white]
		{\tiny$60^\circ$};
	}
\end{tikzpicture}

\only<1>{正三角形を基準にすると、もう少し入るかも…}
\only<2>{XDの長さを求める}
\only<3>{CDは半径の$2$倍なので\(5\ \textrm{cm}\)}
\only<4>{正三角形の高さは\(2.5\sqrt{3}\ \textrm{cm}\)}
\only<5>{よって\( \text{XC}=10-(2.5+2.5+2.5\sqrt{3}) \)

	\hspace*{4.5em}\( =5-2.5\sqrt{3} \)
	}
\only<6>{三平方の定理より\vskip-3ex

	\[ \text{XC}^2+\text{XD}^2=\text{CD}^2 \]
	}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small コマ大数学科 DVD BOX$1$、$1$限目、問\ajMaru{5}ケプラー予想}
\vspace*{-2zh}
\begin{eqnarray*}
(5-2.5\sqrt{3})^2+\text{XD}^2 &=& 5^2 \\
\text{XD}^2 &=& 5^2-(5-2.5\sqrt{3})^2 \\
\text{XD}^2 &\fallingdotseq& 24.5512\cdots \\
\text{XD}^{\phantom{2}} &\fallingdotseq& 4.955 \\
\end{eqnarray*}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small コマ大数学科 DVD BOX$1$、$1$限目、問\ajMaru{5}ケプラー予想}
\begin{tikzpicture}[scale=0.45, thick, >=stealth,
	gbb/.style={fill=white,inner sep=1pt}]
\coordinate [label=left:{\tiny A}] (A) at (2.5,2.5);
\coordinate [label=below:{\tiny B}] (B) at (7.5,2.5);
\coordinate [label=left:{\tiny C}] (C) at ($ (5,{2.5*sqrt(3)+2.5}) $);
\coordinate [label=above:{\tiny D}]
	(D) at ($ ({5+sqrt(5^2-(5-2.5*sqrt(3))^2)},7.5) $);
\coordinate [label=above:{\tiny E}] (E) at ($ (D)+(5,0) $);
\coordinate [label=below:{\tiny F}] (F) at ($ (D)+(2.5,{-2.5*sqrt(3)}) $);
\coordinate [label=below:{\tiny G}]
	(G) at ($ (A)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate [label=below:{\tiny H}]
	(H) at ($ (B)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate [label=right:{\tiny I}]
	(I) at ($ (C)+({5+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $);
\coordinate(X) at (5,7.5);

\draw(24,0)--(0,0)--(0,10)--(24,10);
\foreach \a in {A,...,I}{\fill(\a) circle(3pt);
	\draw (\a) circle (2.5);
	}
\draw[CUDBlue](A)--(B)--(C)--cycle
	(D)--(E)--(F)--cycle
	(G)--(H)--(I)--cycle;

\fill(X) circle (3pt);
\draw(X) node[left,yshift=3pt]{\tiny X};
\draw[CUDGreen](C)--(X)--(D)--cycle
	(X) rectangle ++(9pt,-9pt);

\draw[CUDRed, <->](0,9)-- node[gbb]{\tiny\( 5\ \textrm{cm} \)}(5,9);
\draw[CUDRed, <->]($ ({10+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},9) $)
	--node[gbb]{\tiny\( 5\ \textrm{cm} \)}++(5,0);
\draw[CUDRed](5,0)--(5,10)--($ ({10+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},10) $)--
	($ ({10+2*sqrt(5^2-(5-2.5*sqrt(3))^2)},0) $)--cycle;
\draw[CUDRed, <->, very thick](C)
	-- node[gbb]{\tiny\( 14.90985\ \textrm{cm} \)}(I);
\draw[dashed]($ ({10+2*sqrt(5^2-(5-2.5*sqrt(3))^2)+5},9.5) $)--++(0,-9);
\end{tikzpicture}

{\small
CIの長さは約\(14.90985\ \textrm{cm}\)となり、この幅に円$6$個分入る。\pause
両サイドの\(5+5\ \textrm{cm}\)に円が$3$個分入る。
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}[t]
\frametitle{\small コマ大数学科 DVD BOX$1$、$1$限目、問\ajMaru{5}ケプラー予想}
\( (502.5-(5+5))\div 14.90985 \fallingdotseq 33.03\cdots\)となるので\pause 

\bigskip
円の個数は\( 33\times6\text{個分}+3\text{個分}=201\text{個} \)となる。

\vskip3ex
\centerline{\□答\quad $201$個}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\end{document}



