right triangle in non euclidean geometry

So how do you measure a very big triangle in the Universe? That will be discussed as well, since it is something that NASA's Microwave Anisotrophy Probe (MAP) mission will do in the next few years. Every triangle will give the result of 180 degrees if you measure just a teeny tiny part of a very big space.no matter what its curvature is. Of course, we can't measure just ANY triangle.we have to use a very big triangle in order to be able to discern the shape of the Universe. Depending on the shape of the Universe, the sum will be either less than, equal to, or greater than 180 degrees. In this lesson, we will explore one possible way to measure the curvature of the Universe, namely, by measuring the sum of the angles in a triangle in the Universe. So, it is of more than just a passing fancy that we might want to measure the curvature of the Universe. To a certain degree, the curvature the Universe has depends on how much mass there is in the Universe.and the amount of mass will determine its ultimate fate.

Or it can have a negative curvature, like the middle part of a horse's saddle.

Or it can have a positive curvature, like a sphere. The Universe can be flat, like a piece of paper. For many years, scientists have proposed that there are three possibilities for the curvature (or shape) of the Universe. What is the shape of the Universe? An interesting question, for sure, and one that carries with it other implications - like what the ultimate fate of the Universe will be. Geometry In Space Activity Geometry In Space

Right triangle in non euclidean geometry