A Different Angle

We learn in school that the measures of the interior angles of a triangle add up to 180 degrees.  Did you know that triangles on surfaces other than planes can have different sums?  The interior angles of a triangle on a sphere add up to more than 180 degrees, and the interior angles of a triangle on a pseudosphere add up to less than 180 degrees.  Why would anyone care?  Well, a triangle on a plane is a good study when doing calculations on a local area on the ground, such as what surveyors do.  Triangles on a sphere (elliptical geometry) give part of the picture of what is happening on our big ball of a planet.  Triangles on a pseudosphere (hyperbolic geometry) give part of the picture of what is happening to particles traveling in space.  It’s all relative, m’dear!

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