Math CentralQuandaries & Queries


Question from Joan, a teacher:

What is the min and max number of obtuse angles possible ia a convex quadrilateral in Spherical Geometry?
I know that the Saccheri has 2 obtuse angles and the Lambert has one, but are there other possibilities?
Thanks for your help.


Take four points on the equator -- that's a quadrilateral with four angles of 180 degrees. If you are not happy with that quadrilateral, you can take the points just above the equator and then have four angles that are nearly 180 degrees. In other words, a quadrilateral can have 4 obtuse angles. (As you point out, any quadrilateral on the sphere must have at least one obtuse angle.)


About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS