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File:Fermat Point Proof.svg

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Original file (SVG file, nominally 350 × 400 pixels, file size: 29 KB)

Summary

Description

Proving the construction of Fermat Point is valid: We have to prove the three lines constructed are concurrent. The red and blue triangle are congruent by S.A.S. , and hence the angles in the same segment are the same, which shows that there are two cyclic quadrilaterals. Thus the last four points are also concyclic, and by angle in the same segment the last line is a straight line.

N.B. all information are included in the metadata of this svg file.
Date 11 March 2006 (original upload date)
Source No machine-readable source provided. Own work assumed (based on copyright claims).
Author No machine-readable author provided. Lemontea~commonswiki assumed (based on copyright claims).

Source

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

fermat_point_proof.euk

frame(-2.8, -6, 8.2, 7.5)
B C A triangle(6, 75:, 35:)
C B P equilateral
A C Q equilateral
B A R equilateral
s = segment(A, P)
t = segment(B, Q)
u = segment(C, R)
c = circle(B, A, R)
d = circle(A, C, Q)
e = circle(C, B, P)
F = intersection(line(A, P), line(B, Q))

color(green)
draw(c)
color(cyan)
draw(d)
color(blue)
draw(t)
draw(segment(A, Q))
draw(segment(A, B))
mark(segment(A, B), simple)
mark(segment(A, Q), double)
mark(B, A, Q, simple, 1.2)
color(red)
draw(u)
draw(segment(A, R))
draw(segment(A, C))
mark(segment(A, R), simple)
mark(segment(A, C), double)
mark(R, A, C, simple, 0.8)
color(black)
draw(s)
draw(segment(B, R))
draw(segment(C, Q))
draw(C, B, P)
draw(e, dashed)
draw(F, dot, 1.3)
mark(segment(B, R), simple)
mark(segment(C, Q), double)
mark(segment(B, C), triple)
mark(segment(B, P), triple)
mark(segment(C, P), triple)
mark(C, R, A, double, 1.5)
mark(Q, B, A, double, 1.5)
mark(A, Q, B, triple, 1.5)
mark(A, C, R, triple, 1.5)
mark(B, F, P, dot, 0.8)
mark(B, C, P, dot, 0.8)
label(F, 0.5, 0:)
label(A, 0.5, 90:)
label(B, 0.5, 225:)
label(C, 0.5, 330:)
label(P, 0.3, 270:)
label(Q, 0.3, 0:)
label(R, 0.3, 90:)

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.

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head 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.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This licensing tag was added to this file as part of the GFDL licensing update.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.

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depicts

11 March 2006

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Date/TimeThumbnailDimensionsUserComment
current01:22, 11 March 2006Thumbnail for version as of 01:22, 11 March 2006350 × 400 (29 KB)Lemontea~commonswikiProving the construction of Fermat Point is valid: We have to prove the three lines constructed are concurrent. The red and blue triangle are congruent by S.A.S. , and hence the angles in the same segment are the same, which shows that there are two cycl

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