Applications of Hyperbolic Space

[Treadstone]

...are there any?

 

Nathan

[violetendncy]

In physics, until we figure out whether or not the expansion of the universe is decelerating (this would be the non-euclidean elliptic geometry), Hyperbolic geometry could be the most accurate way to define the geometries of fields (like gravity) etc.

[matt grime]

Hyperbolic geometry is the most prevalent form of geometry in applications (eg GR, SR, whatever the physics is). Euclidean geometry, whilst apparently the most useful, turns out to be the least interesting. You may wish to learn about Riemann surfaces and quotients by actions of groups to see why this apparently odd statement is actually very natural.