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December 1, 2020 17:29
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Diagram of geodesics in the Poincare Upper Half-Plane
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%% -------------------------------------------------------------- | |
%% Code for the diagram in a twitter thread about Lobachevsky. | |
%% Tweet: https://twitter.com/mcnees/status/1333812403218354177 | |
%% -------------------------------------------------------------- | |
\documentclass[crop=true, border=10pt]{standalone} | |
\usepackage{amsmath} | |
\usepackage{amsfonts} | |
\usepackage{mathrsfs} | |
\usepackage{graphicx} | |
\usepackage{xcolor} | |
\usepackage{tikz} | |
\usetikzlibrary{arrows.meta} | |
\usetikzlibrary{decorations.markings} | |
\usepackage{tikz-3dplot} | |
\usepackage{pgfplots} | |
% A few colors | |
%-------------------------------------------------------------- | |
\definecolor{plum}{rgb}{0.36078, 0.20784, 0.4} | |
\definecolor{chameleon}{rgb}{0.30588, 0.60392, 0.023529} | |
\definecolor{cornflower}{rgb}{0.12549, 0.29020, 0.52941} | |
\definecolor{scarlet}{rgb}{0.8, 0, 0} | |
\definecolor{brick}{rgb}{0.64314, 0, 0} | |
\definecolor{sunrise}{rgb}{0.80784, 0.36078, 0} | |
\definecolor{lightblue}{rgb}{0.15,0.35,0.75} | |
%\pgfplotsset{width=7cm,compat=1.15} | |
\begin{document} | |
\pagestyle{empty} | |
%\begin{center} | |
\begin{tikzpicture}[scale=1.25,domain=0:13] | |
\tikzstyle{axisarrow} = [-{Latex[inset=0pt,length=7pt]}] | |
% Clip all lines that would fall outside the grid | |
\clip(-2,-1.25) rectangle (6,4); | |
% \draw[fill=plum!40,opacity=0.2] (4,-2) -- (8,-2) -- (8,13) -- (4,13) -- (4,-2); | |
% \draw[fill=scarlet!40,opacity=0.2] (-2,-10/4) -- (1,-10/4) -- (13.4,13) -- (10.4,13) -- (-2,-10/4); | |
% Draw the grid. | |
\draw [cornflower!30,step=0.2,thin] (-2,0) grid (6,4); | |
\draw [cornflower!60,step=1.0,thin] (-2,0) grid (6,4); | |
% \node[] at (6,-0.5) {Barn}; | |
% \node[] at (1.25,-0.5) {Pole}; | |
% Draw Axes | |
\draw[thick,axisarrow] (-1,-1) -- (-1,4); | |
\node[inner sep=0pt] at (-0.66,3.7) {$y$}; | |
\draw[thick,axisarrow] (-2,0) -- (6,0); | |
\node[inner sep=0pt] at (5.75,+0.33) {$x$}; | |
\draw [scarlet,thick,domain=1:3,samples=200] plot ({\x}, {sqrt(-(\x-2)^2 + 1 + (2-2)^2 )}); | |
\draw [sunrise,thick,domain=1.3820:3.618,samples=200] plot ({\x}, {sqrt(-(\x-2.5)^2 + 1 + (2-2.5)^2 )}); | |
\draw [chameleon,thick,domain=1.586:4.414,samples=200] plot ({\x}, {sqrt(-(\x-3)^2 + 1 + (2-3)^2 )}); | |
\draw [plum,thick,domain=1.6973:5.303,samples=200] plot ({\x}, {sqrt(-(\x-3.5)^2 + 1 + (2-3.5)^2 )}); | |
\node at (2,1) [circle,draw=cornflower!70,fill=cornflower!20,inner sep=1pt] {}; | |
\node at (1.9,1.2) [] {$P$}; | |
\node at (0.25,2.15) [] {$L$}; | |
\draw[brick,thick] (0,0) -- (0,4); | |
\node at (1,-0.5) [] {$\displaystyle ds^2 = \frac{1}{y^2}\,(dx^2 + dy^2)$}; | |
\node at (3.62,-0.5) [] {$\displaystyle x'(s) = c\,\,y(s)^2$}; | |
\node at (4.25,-1) [] {$\displaystyle y'(s) = \sqrt{y(s)^2 - c^2\,y(s)^4}$}; | |
\end{tikzpicture} | |
%\end{center} | |
\end{document} |
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