Image:Fermat Point Derivation.svg

[edit] Summary

Arriving at the solution of minimizing total distance from a point to the three vertex of a given triangle(Fermat's Problem) :

Rotate one side of the triangle with the arbitary point F for 60 degrees, and the distance to minimize is the shortest path from A to D. Hence the solution is when it become a straight line.

N.B. all information are included in the metadata of this svg file.

[edit] Source

The source is licensed under the same license as the image. Feel free to edit, fix, or improve it!

[edit] fermat_point_derivation.euk

frame(-0.5, -6, 7, 4.5)
B C A triangle(6, 75:, 35:)
C B D equilateral
F = point(2.5, 35:)
F B G equilateral

color(black)
draw(segment(A, B))
draw(segment(A, C))
thickness(2)
draw(segment(A, F))
draw(segment(F, G), dashed)
thickness(0.5)
draw(segment(C, D), dashed)

color(red)
draw(B, C, F)
color(blue)
draw(B, D, G)
thickness(2)
draw(segment(G, D))
thickness(0.5)

color(red)
mark(segment(B, F), simple)
mark(segment(F, C), double)
mark(segment(B, C), triple)

color(blue)
mark(segment(B, G), simple)
mark(segment(G, D), double)
mark(segment(B, D), triple)

color(black)
mark(segment(F, G), simple)
mark(D, B, C, simple, 0.8)
mark(G, B, F, simple, 1.5)

label(A, 0.2, 90:)
label(B, 0.2, 180:)
label(C, 0.2, 0:)
label(D, 0.2, 270:)
label(F, 0.2, 30:)
label(G, 0.2, 0:)

[edit] Instruction

1. Run eukleides and compile it into en:PSTricks.
2. Paste the resulting code in the following en:TeX file and compile it into eps.

\documentclass{article}
\usepackage{pstricks}
\usepackage{color}

\begin{document}
\pagestyle{empty}
\colorbox{white}{

%Paste the code here

}
\end{document}

1. Import the eps file using en:Scribus. (Remember to install en:ghostscript also and configure the path to ghostscript correctly in Scribus's Preferences)
2. And then export it to en:svg.
3. Post-process using en:Inkscape.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses: 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". Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/- This file is licensed under the Creative Commons Attribution ShareAlike license versions 2.5, 2.0, and 1.0 العربية | Български | Català | Česky | Dansk | Deutsch | English | Español | Euskara | فارسی | Français | עברית | Italiano | 日本語 | 한국어 | Lietuvių | Nederlands | Polski | Português | Русский | Svenska | தமிழ் | Türkçe | 中文 | 中文 | +/- You may select the license of your choice.

• Fermat point