Three Spherical Triangles of Equal Area

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This Demonstration shows three spherical triangles. Triangles and have a common base and the same area, so they are equivalent by dissection (as shown in Dissection of Two Spherical Triangles with a Common Base). Triangles and also have a common base and the same area, so they are also equivalent by dissection. So triangles and are equivalent by dissection.

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Therefore, spherical triangles with the same area are equivalent by dissection.

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


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References

[1] P. Gerwien, "Zerschneidung jeder beliebigen Anzahl von gleichen geradlinigen Figuren in dieselben Stücke," Journal für die reine und angewandte Mathematik (Crelle's Journal), 10, 1833 pp. 228–234, and Taf. 3. gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002139170.

[2] Wikipedia. "Saccheri Quadrilateral." (Mar 20, 2017) en.wikipedia.org/wiki/Saccheri_quadrilateral.



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