Euclid's Postulates

Core concept

Euclid's fifth postulate, more complex than the others, essentially states that if a line crosses two other lines making the interior angles on one side sum to less than 180°, those two lines will eventually meet on that side if extended far enough — this postulate was historically debated by mathematicians for centuries, since it seemed less 'self-evident' than the others, eventually leading to the development of non-Euclidean geometries where this postulate does not hold.