Generalized Spherical Triangles

 

Further subjects are under  miscellaneous mathematics and Geometric algebra.

Generalized Spherical Triangles

The purpose is to introduce spherical triangles with one ore more angles or sides greater than pi. A signed area theory extends  with a little modification the connection between area and spherical excess , and facilitates a classification of the triangles.
The triangle cases  are investigated. Formulae for the radii of circumcircles , in- and excircles are found.
Also the assignment problem for incircles is solved. A duality theorem is proved.

The content of the work starts with some basic theory regarding the subject. To get an overview of the contents of the work it is listed in a bulleted list below:

  1. The basic theory.
  2. GST problems and solutions.
  3. Examples.
  4. Theory for the GST cases.
  5. The Circumcircle.
  6. Area.
  7. In- and Excircles.
  8. Duality.
  9. Miscellaneous.
  10. References.

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