If projective geometry, through its principle of duality, has enormously enriched mathematics from an aesthetic point of view, the creation of non-Euclidean geometry has had an unparalleled intellectual impact on our entire scientific and philosophical thought. It marked the first serious doubt since Euclid’s time as to the validity of our fundamental mathematical premises; it shattered the age-old belief in the power of mathematics to show us the road to the ultimate and absolute truth; and it brought about a whole reexamination of our ability to understand the physical world in which we live. This reexamination has had consequences which far transcended mathematics; ultimately, it led to the theory of relativity and helped in shaping our modern views of the universe. The spark that ignited this intellectual revolution was once again the infinite; more specifically, the question: What happens to parallel lines very far away?
KeywordsPhysical World Great Circle Elliptic Geometry Euclidean Geometry Projective Geometry
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