File:Archimedean property for Achilles and Tortoise example.svg
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Original file (SVG file, nominally 533 × 147 pixels, file size: 34 KB)
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Summary
| Description |
English: An illustration of the Archimedean property of real numbers. Achilles starts the race at the initial point mathP_0</math>, and the tortoise at mathP_1</math>. They finish the race at the same time. When Achilles reaches mathP_1</math>, the tortoise reaches mathP_2</math>, etc. The Archimedean property is that any point x in the race lies between two of the P's.The following code was generated using conversion to TiKZ, and manual adjustment so that the generated PDF looks nice. |
| Date | |
| Source | Created with GeoGebra |
| Author | Sławomir Biały |
\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{yqqqqq}{rgb}{0.5019607843137255,0.,0.}
\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1.}
\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm,scale=10]
\clip(-0.12424528781181865,-0.15367169638774447) rectangle (1.379623024945378,0.2598262459990889);
\draw [line width=2.pt] (0.,0.)-- (1.,0.);
\draw (0.4762485393486732,0.08) node[anchor=north west] {$P_1$};
\draw (-0.024162983285070005,0.08) node[anchor=north west] {$P_0$};
\draw (0.7185530660976437,0.08) node[anchor=north west] {$P_2$};
\draw (0.8370715846161618,0.08) node[anchor=north west] {$P_3$};
\draw (0.9081826957272727,0.08) node[anchor=north west] {$P_4$};
\draw (0.9481826957272727,0.07) node[anchor=north west] {$\dots$};
\draw (0.884478992023569,-0.01) node[anchor=north west] {$x$};
\begin{scriptsize}
\draw [fill=uuuuuu] (0.,0.) circle (0.25pt);
\draw [fill=uuuuuu] (1.,0.) circle (0.25pt);
\draw[color=uuuuuu] (1.1188822842046382,0.016204846822132895) node {Finish line};
\draw [fill=xdxdff] (0.9108164405832435,0.) circle (0.2pt);
\draw [color=yqqqqq, very thick] (0.,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.5,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.75,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.9375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.96875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.984375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.9921875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.99609375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.998046875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.9990234375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.99951171875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.999755859375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.9998779296875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.99993896484375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\draw [color=yqqqqq, very thick] (0.999969482421875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);
\end{scriptsize}
\end{tikzpicture}
\end{document}
Licensing
Sławomir Biały at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
Attribution: Sławomir Biały at English Wikipedia
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 2017-07-25 11:34:45 | 533 × 147 | Sławomir Biały | Uploading a self-made file using [[Wikipedia:File_Upload_Wizard|File Upload Wizard]] |
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:38, 15 December 2018 | | 533 × 147 (34 KB) | I love rpgs | Transferred from en.wikipedia (MTC!) (1.1.0) |
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