Projective Geometry
This axiom is specific to Euclidean geometry only.
What is the parallel postulate?
This concept, which relates to the ratios of sides and angles of a shape, is not preserved in hyperbolic geometry.
What is similarity?
Is the geometry of the two-dimensional surfaces of spheres
What is Spherical Geometry?
If physical space was Euclidean, we would only know things in this way.
What is locally?
This is the only axiom that differs from Euclidean geometry.
What is the parallel postulate?
the shortest possible line between two points on a sphere
What is a Geodesic?
These types of constructions are not used in projective geometry.
What are compass constructions?
The angle sum of triangles relates directly to this quantity.
What is the area?
Spherical Geometry is a sub-category of this geometry
What is Non-Euclidian?
These basics of Euclidean geometry are applicable to all geometries, including those that are non-Euclidean.
What are the common notions?
This model for viewing hyperbolic geometry is named after one of the key proponents of geometric conventionalism.
What is the Poincaré Disk Model?
All longitude lines are examples of this spherical geometry term.
What are great circles?
N-th dimensional geometry was formed from projective geometry through this process.
What is axiomation?
This measured property of a circle is greater than its Euclidean counterpart.
The circumference
An infinite many of great circles can be drawn through which two points.
What are the poles?