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Without words: an arctan identity 

arctan 1/8 + pi/4 + arctan 1/7 + arctan 4/7 = pi /2
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ulaulaman 2020-08-03 22:59:05 +02:00
parent 425a174021
commit cc154f9816
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math/arctan-pi2.tex Executable file
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\documentclass{standalone}
%
\usepackage{tikz}
\usetikzlibrary{backgrounds,calc}
\usepackage{tkz-euclide}
\usetkzobj{all}
%
\usepackage{amsmath}
%
\usepackage{xcolor}
%
\definecolor{space}{HTML}{0A2543}
\definecolor{earth}{HTML}{0089FA}
\definecolor{mars}{HTML}{DC7B4E}
\definecolor{dida}{HTML}{FFDE00}
\definecolor{moon}{HTML}{AFAFAF}
%
\usepackage{fontspec}
\setmainfont{Open Dyslexic}
%
\title{Trigonometry: ArcTan pi/2}
\begin{document}
\begin{tikzpicture}[background rectangle/.style={fill=white},show background rectangle]
%
\begin{scope}[scale=8]
\tkzDefPoint(0,0){O}
\tkzDefPoint(56,0){A}
\tkzDefPoint(56,7){B}
\tkzDrawSquare[fill=space](O,A)
%
\tkzDrawPolygon[fill=earth, opacity=0.7](O,A,B)
%
\tkzDefPoint(56,56){C}
\tkzDefPointBy[rotation = center O angle {atan(1/8)}](C) \tkzGetPoint{C1}
\tkzDefPointBy[rotation = center O angle {atan(1/8)}](A) \tkzGetPoint{A1}
\tkzDrawPolygon[fill=mars, opacity=0.7](O,A1,C1)
%
\tkzDefPoint(56,8){D}
\tkzDefPointBy[rotation = center O angle {atan(1/8)+45}](D) \tkzGetPoint{D1}
\tkzDefPointBy[rotation = center O angle {45}](A1) \tkzGetPoint{A2}
\tkzDrawPolygon[fill=dida, opacity=0.7](O,A2,D1)
%
\tkzDefPoint(56,32){E}
\tkzDefPointBy[rotation = center O angle {atan(1/8)+45+atan(1/7)}](E) \tkzGetPoint{E1}
\tkzDefPointBy[rotation = center O angle {atan(1/7)}](A2) \tkzGetPoint{A3}
\tkzDrawPolygon[fill=moon, opacity=0.7](O,A3,E1)
%
\tkzLabelSegment[black,below=5ex,pos=.5](O,A){\fontsize{299}{300}\selectfont 56}
\tkzLabelSegment[black,right=5ex,pos=.5](A,B){\fontsize{299}{300}\selectfont 7}
\tkzLabelSegment[white,above=10ex,pos=.5](O,A1){\fontsize{299}{300}\selectfont 56}
\tkzLabelSegment[white,right=10ex,pos=.5](A1,C1){\fontsize{299}{300}\selectfont 56}
\tkzLabelSegment[white,below=10ex,pos=.5](O,A2){\fontsize{299}{300}\selectfont 56}
\tkzLabelSegment[white,right=10ex,pos=.5](A2,D1){\fontsize{299}{300}\selectfont 8}
\tkzLabelSegment[white,above=20ex,pos=.5](O,A3){\fontsize{299}{300}\selectfont 56}
\tkzLabelSegment[black,right=20ex,pos=.6](A3,E1){\fontsize{299}{300}\selectfont 32}
%
\node at (28,-3) {\textcolor{black}{\fontsize{299}{300}\selectfont Arctan 1/8 + pi/4 + Arctan 1/7 + Arctan 4/7 = pi/2}};
\end{scope}
%
\end{tikzpicture}
\end{document}

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math/pdf/arctan-pi2.pdf Normal file
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