World Science Scholars
4.3 Non-Euclidean Geometry

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The general theory of relativity allows for the possibility that our universe is not “flat,” but instead some other, non-Euclidean geometry, such as the surface of a sphere (a “closed” geometry). How could we test if our universe exists in a closed or flat geometry? One way is to consider specific shapes and examine their properties when projected into different geometries. In this demonstration, you create a triangle in flat geometry using the sliders on the left. Note how its angles will always add up to 180°. Then, the triangle is projected onto the surface of a sphere, stretching the shape and skewing the angles in such a way that the angles will always add to more than 180°, helping to differentiate the two example geometries.

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