Dissection of Gerwien's Triangle into a Saccheri Quadrilateral on the Sphere

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This Demonstration shows Gerwien's dissection of a spherical triangle into a spherical Saccheri quadrilateral. Two cases are treated, namely that from Figures 1 and 3 from Gerwien's 1833 article [1].

Contributed by: Izidor Hafner (May 2017)
Open content licensed under CC BY-NC-SA


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A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base [2].

References

[1] P. Gerwien, "Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke," Journal für die reine und angewandte Mathematik (Crell's Journal), 10, pp. 228–234, and Taf. 3. gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002139170.

[2] Wikipedia. "Saccheri Quadrilateral." (May 1, 2017) en.wikipedia.org/wiki/Saccheri_quadrilateral.



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