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Results tagged with mg.metric-geometry
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user 51484
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
7
votes
Is every elementary absolute geometry Euclidean or hyperbolic?
The answer is yes. The completion of a semi-elliptic plane is hyperbolic. The name probably comes from the fact that each pair of lines in it has either a point or a single perpendicular in common (in …
- 1,731
9
votes
1
answer
725
views
Is there a straightedge and compass construction of incommensurables in the hyperbolic plane?
In other words, given a segment in the hyperbolic plane is there a straightedge and compass construction of a segment incommensurable with it? In the Euclidean plane one can take the diagonal of the s …
- 1,731
22
votes
2
answers
2k
views
Is every elementary absolute geometry Euclidean or hyperbolic?
Absolute geometry is any one that satisfies Hilbert's axioms of plane geometry without the axiom of parallels. It is well-known that it is either the Euclidean or a hyperbolic plane. For an elementary …
- 1,731