File:Fermat Point.svg

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Description Constructing the Fermat Point of a given triangle: Draw three regular triangles on each side of it, join their outlying vertex with the opposite triangle's vertex, and the lines intersect at the Fermat Point. Note that this point is a valid solution to the shortest total distance problem only for triangle with the greatest angle less then 120 degrees. N.B. all information are included in the metadata of this svg file. 
 frame(-3.5, -6, 7.5, 7) 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) F = intersection(line(A, P), line(B, Q)) color(red) thickness(2) draw(s) draw(t) draw(u) draw(F) thickness(0.5) color(black) thickness(4) draw(B, C, A) thickness(0.25) draw(B, C, P, dashed) draw(A, C, Q, dashed) draw(B, A, R, dashed) mark(segment(A, B), simple) mark(segment(A, R), simple) mark(segment(B, R), simple) mark(segment(A, C), double) mark(segment(A, Q), double) mark(segment(C, Q), double) mark(segment(B, C), triple) mark(segment(B, P), triple) mark(segment(C, P), triple)
# Run eukleides and compile it into en:PSTricks. # 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}
# Import the eps file using en:Scribus. (Remember to install en:ghostscript also and configure the path to ghostscript correctly in Scribus's Preferences) # And then export it to en:svg. # Post-process using en:Inkscape.
Source The source is licensed under the same license as the image. ; Feel free to edit, fix, or improve it!
Author Lemontea

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This licensing tag was added to this file as part of the GFDL licensing update.
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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.
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current01:20, 11 March 2006Thumbnail for version as of 01:20, 11 March 2006350 × 400 (11 KB)Lemontea~commonswiki (talk | contribs)Constructing the Fermat Point of a given triangle: Draw three regular triangles on each side of it, join their outlying vertex with the opposite triangle's vertex, and the lines intersect at the Fermat Point. Note that this point is a valid solution to

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