The Geometry of Hyperparallelism

One of the most common families of non-Euclidean geometry is hyperbolic geometry – a self-consistent geometry of “obtuse” curvature.

While “normal,” foundational Euclidean geometry was founded upon five fundamental principles (Euclid’s five axioms), it is the fifth and final principle – the so-called parallel postulate – which is used to differentiate between this and any non-Euclidean space.

This principle defines, simply enough, that two lines are parallel to each other when a third line drawn between them will create angles which add up to exactly 180 degrees on each side. When any sort of space with curvature is considered, however, this postulate no longer holds true (necessarily), and therefore, an entirely new form of geometry must be instated. Continue reading “The Geometry of Hyperparallelism”