Part 2/10:
As we set the stage, the essence of geometry becomes pivotal. Renowned Greek mathematician Euclid established rules that govern our understanding of space, particularly his Parallel Postulate, asserting that parallel lines will always remain equidistant and never meet. Yet, mathematicians, after centuries of contemplation, discovered that under different geometrical frameworks, namely non-Euclidean geometry, parallel lines could interact.
This paradigm shift opened the door to several remarkable cosmic inquiries: What does it mean for our universe if it is expanding? And crucially, what, if anything, is it expanding into?