Positively curved

Definition

Positively curved space refers to a type of geometric curvature where the sum of the angles of a triangle is greater than 180 degrees. This occurs in spherical geometries and is often contrasted with flat or negatively curved spaces.

5 Must Know Facts For Your Next Test

1. In positively curved space, parallel lines eventually converge.
2. The universe may have positive curvature if it has enough mass and energy density to close it upon itself.
3. A positively curved universe is finite but unbounded, meaning you could travel indefinitely without encountering an edge.
4. The concept of positively curved space is crucial in understanding general relativity and cosmology.
5. Measurements of cosmic microwave background radiation help determine whether our universe has positive curvature.

Review Questions

• What happens to parallel lines in a positively curved space?
• How does positively curved space affect the geometry of triangles?
• Why is the concept of positive curvature important in cosmology?

Related terms

Negative Curvature: A type of geometric curvature where the sum of the angles of a triangle is less than 180 degrees, typical in hyperbolic geometry.

Flat Space: A type of geometric curvature where the sum of the angles of a triangle equals exactly 180 degrees, characteristic of Euclidean geometry.

Cosmic Microwave Background (CMB): Radiation left over from the early stages of the universe, crucial for studying its shape and composition.