World Science Scholars
4.3 Non-Euclidean Geometry
demonstration
demonstration

PLEASE NOTE: For better performance, you may download the demonstration by clicking here.
If you have not already downloaded and installed the free CDF player, it is available here.

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.

To load this interactive demonstration, you will need to install Wolfram CDF Player. If you have already installed Wolfram CDF Player and cannot see the demonstration, please try viewing this page in another internet browser.


×

Share with others

Select this checkbox if you want to share this with all users

Select Users

Enter the usernames or email IDs of the users you want to share with

Please enter message

Explain why you want them to see this

Send this to a friend