Negatively curved

Definition

Negatively curved space is a type of non-Euclidean geometry where parallel lines diverge and the internal angles of triangles sum to less than 180 degrees. It is often described using hyperbolic geometry.

5 Must Know Facts For Your Next Test

1. Negatively curved space is represented in hyperbolic geometry.
2. In negatively curved space, the sum of the angles of a triangle is always less than 180 degrees.
3. Parallel lines in negatively curved space diverge rather than converge or remain equidistant.
4. Negatively curved spaces can model certain properties of dark matter distributions in cosmology.
5. The concept of negatively curved space helps in understanding the topology and geometry of the universe.

Review Questions

• What happens to parallel lines in a negatively curved space?
• How do the angles of a triangle behave in negatively curved space?
• Why is understanding negatively curved space important for studying dark matter?

Related terms

Hyperbolic Geometry: A type of non-Euclidean geometry characterized by a constant negative curvature.

Non-Euclidean Geometry: Any type of geometry that is not based on Euclid's postulates, including hyperbolic and elliptic geometries.

Dark Matter: A form of matter thought to account for approximately 85% of the matter in the universe; it does not emit light or energy, making it invisible and detectable only through its gravitational effects.