Three Spherical Triangles of Equal Area

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

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.