One way in which elliptic geometry differs from Euclidean geometry is that the sum of the interior angles of a triangle is greater than 180 degrees.
22.
More generally, the term " motion " is a synonym for surjective isometry in metric geometry, including elliptic geometry and hyperbolic geometry.
23.
Their research uncovered two types of spaces whose geometric structures differ from that of classical Euclidean space; these gave rise to hyperbolic geometry and elliptic geometry.
24.
Absolute geometry is inconsistent with elliptic geometry : in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist.
25.
Absolute geometry is inconsistent with elliptic geometry : in elliptic geometry there are no parallel lines at all, but in absolute geometry parallel lines do exist.
26.
Spherical geometry is " not " elliptic geometry, but shares with that geometry the property that a line has no parallels through a given point.
27.
The parallel property of elliptic geometry is the key idea that leads to the principle of projective duality, possibly the most important property that all projective geometries have in common.
28.
I know that, in elliptic geometry, it's possible to have a triangle with three right angles thus adding up to 270?rather than the Euclidian 180?
29.
Some say one should face the direction which would be the shortest distance to Jerusalem, i . e . the arc of a great circle, as defined in elliptic geometry.
30.
This study became widely accessible through the Poincar?disc model where Riemann, a student of Gauss's, constructed Riemannian geometry, of which elliptic geometry is a particular case.
