# Parallel (geometry)

##### Non-Euclidean geometry

5 months ago**Non-Euclidean geometry** ... of metric **geometry** and affine **geometry**, non-Euclidean **geometry** arises by either relaxing the metric requirement, or replacing the **parallel** postulate with...

##### Euclidean geometry

5 months ago**Euclidean geometry** ... other sort of **geometry** had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the **parallel** postulate) that...

##### Hyperbolic geometry

5 months ago**Hyperbolic geometry** ... mathematics, hyperbolic **geometry** (also called Lobachevskian **geometry** or Bolyai–Lobachevskian **geometry**) is a non-Euclidean **geometry**. The **parallel** postulate of Euclidean...

##### Parallel postulate

5 months ago**Parallel postulate** ... In **geometry**, the **parallel** postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom...

##### Geometry

5 months ago**Geometry** ... and Riemannian **geometry**. Later in the 19th century, it appeared that **geometries** without the **parallel** postulate (non-Euclidean **geometries**) can be developed...

##### Affine geometry

5 months ago**Affine geometry** ... notion of **parallel** lines is one of the main properties that is independent of any metric, affine **geometry** is often considered as the study of **parallel** lines...

##### Elliptic geometry

5 months ago**Elliptic geometry** ... Elliptic **geometry** is an example of a **geometry** in which Euclid's **parallel** postulate does not hold. Instead, as in spherical **geometry**, there are no **parallel** lines...

##### Parallel transport

6 months ago**Parallel transport** ... In **geometry**, **parallel** transport is a way of transporting geometrical data along smooth curves in a manifold. If the manifold is equipped with an affine...

##### Projective geometry

5 months ago**Projective geometry** ... for projective **geometry** was indeed the theory of perspective. Another difference from elementary **geometry** is the way in which **parallel** lines can be said...

##### Absolute geometry

5 months ago**Absolute geometry** ... Absolute **geometry** is a **geometry** based on an axiom system for Euclidean **geometry** without the **parallel** postulate or any of its alternatives. Traditionally...