Dissection of a Composite Spherical Triangle

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This Demonstration shows a dissection and reassembly of a spherical triangle, maintaining the same base and area. We begin with the composite triangle and reassemble it into the composite triangle . The motion is guided by circles, which can be shown.

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



This dissection is based on the fact that the triangles have a common Saccheri quadrilateral.

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


[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, 1833 pp. 228–234, and Taf. 3. gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002139170.

[2] Wikipedia. "Saccheri Quadrilateral." (May 4, 2017) en.wikipedia.org/wiki/Saccheri_quadrilateral.

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