From 2faef9cb41cca40a8c1a21096462045633841ead Mon Sep 17 00:00:00 2001 From: ulaulaman Date: Mon, 3 Aug 2020 22:00:39 +0200 Subject: [PATCH] Without words: arctan 1/2 + arctan 1/3 = pi/4 --- math/arctan-pi4.tex | 44 ++++++++++++++++++++++++++++++++++++++++ math/pdf/arctan-pi4.pdf | Bin 0 -> 26695 bytes 2 files changed, 44 insertions(+) create mode 100755 math/arctan-pi4.tex create mode 100644 math/pdf/arctan-pi4.pdf diff --git a/math/arctan-pi4.tex b/math/arctan-pi4.tex new file mode 100755 index 0000000..84989ac --- /dev/null +++ b/math/arctan-pi4.tex @@ -0,0 +1,44 @@ +\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} +% +\title{Trigonometry: ArcTan pi/4} +\begin{document} + \begin{tikzpicture}[background rectangle/.style={fill=white},show background rectangle] + % + \begin{scope}[scale=8] + \tkzDefPoint(0,0){O} + \tkzDefPoint(2,0){A} + \tkzDefPoint(2,1){B} + \tkzDrawSquare[fill=space](O,A) + % + \tkzDrawPolygon[fill=earth](O,A,B) + % + \tkzDefPoint(3,0){C} + \tkzDefPoint(3,1){D} + \tkzDefPointBy[rotation = center O angle {atan(1/2)}](C) \tkzGetPoint{C1} + \tkzDefPointBy[rotation = center O angle {atan(1/2)}](D) \tkzGetPoint{D1} + % + \tkzDrawPolygon[fill=mars](O,C1,D1) + % + \tkzLabelSegment[black,below=2ex,pos=.5](O,A){\fontsize{17}{18}\selectfont $2$} + \tkzLabelSegment[black,right=2ex,pos=.5](A,B){\fontsize{17}{18}\selectfont $1$} + \tkzLabelSegment[black,below=2ex,pos=0.8](O,C1){\fontsize{17}{18}\selectfont $3$} + \tkzLabelSegment[black,right=2ex,pos=.5](C1,D1){\fontsize{17}{18}\selectfont $1$} + % + \node at (0.5,1.5) {\textcolor{white}{\fontsize{17}{18}\selectfont $\arctan \frac{1}{2} + \arctan \frac{1}{3} = \frac{\pi}{4}$}}; + \end{scope} + % + \end{tikzpicture} +\end{document} \ No newline at end of file diff --git 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