# Thomsen's Figure

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Thomsen's figure is illustrated by the following process. For any triangle , pick a point on opposite . From , draw a line segment parallel to intersecting at point , then from there a segment parallel to intersecting at . Continue through the figure. Thomsen's theorem states that the final segment from parallel to terminates at the original point .

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Drag the triangle vertices , and to illustrate the diagram for different triangles. The slider moves between the vertices and .

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Contributed by: Robert Dickau (August 2022)
Open content licensed under CC BY-NC-SA

## Details

References

[1] Wikipedia. "Thomsen's Theorem." (Jan 26, 2022) en.wikipedia.org/wiki/Thomsen%27s_theorem.

[2] "Thomsen's Theorem." Futility Closet. (Jan 26, 2022) www.futilitycloset.com/2021/06/24/thomsens-theorem.

[3] E. W. Weisstein. "Thomsen's Figure." (Jan 26, 2022) Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/ThomsensFigure.html (Wolfram MathWorld).

[4] E. W. Weisstein. "Thomsen's Figure." (Jan 26, 2022) archive.lib.msu.edu/crcmath/math/math/t/t137.htm (same as [3], except MW description is wrong).

[5] Wikipedia. "Pappus's Hexagon Theorem." (Jan 26, 2022) en.wikipedia.org/wiki/Pappus%27s_hexagon_theorem#Dual_theorem.

## Permanent Citation

Robert Dickau "Thomsen's Figure"
http://demonstrations.wolfram.com/ThomsensFigure/
Wolfram Demonstrations Project
Published: August 16, 2022

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