Thomsen’s Figure

Thomsen’s figure, or Thomsen’s theorem, illustrates the following process: For any triangle ABC, pick a point A1 on BC opposite A. From A1 draw a line segment parallel to AB intersecting AC at point B1; then from there a segment parallel to BC intersecting AB at C1; continuing through the figure. Thomsen’s theorem shows that the final segment from C2 parallel to AC meets at the original point A1.

You might enjoy the interactive Wolfram Demonstrations Project version.

Is there some reason this wouldn’t work for any polygon with an odd number of sides?


Designed and rendered using Wolfram Mathematica 13.
First draft December 2021 by Robert Dickau.

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