Thomsen's Figure

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .


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


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




[1] Wikipedia. "Thomsen's Theorem." (Jan 26, 2022)

[2] "Thomsen's Theorem." Futility Closet. (Jan 26, 2022)

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

[4] E. W. Weisstein. "Thomsen's Figure." (Jan 26, 2022) (same as [3], except MW description is wrong).

[5] Wikipedia. "Pappus's Hexagon Theorem." (Jan 26, 2022)

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.