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Thomsen's theorem, named after Gerhard Thomsen, is a theorem in elementary geometry. It shows that a certain path constructed by line segments being parallel to the edges of a triangle always ends up at its starting point.
geodesic sphere {3,5+} 3,3: 282 37147.294418462 0 0 0 12 270 0 0 840 560 0 12.166° geodesic sphere {3,5+} 4,2: 292 39877.008012909 0 0 0 12 280 0 0 870 580 0 11.857° 306 43862.569780797 0 0 0 12 294 0 0 912 608 0 11.628° 312 45629.313804002 0.000306163 0 0 12 300 0 0
Thomsen wrote 22 papers on various topics in geometry and furthermore a few papers on theoretical physics as well. The latter were mostly written in Italian rather than in German. Thomsen also wrote a book on the foundations of elementary geometry. [1] In elementary geometry Thomsen's theorem is named after him. [5]
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The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of A B C {\displaystyle ABC} and a b c {\displaystyle abc} . [ 3 ]
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