Development of the Projective Disc and its Applications, 1868-2015

Abstract

In the late 19th century, the projective disc arose as a Euclidean model for nonEuclidean geometry. To understand this development, however, one must first examine the concept of Euclidean geometry itself. A fundamental principle of mathematics is the notion of creating and evaluating statements, and attempting to prove that they are in fact true, while rejecting them if they cannot be proven true or are proven to be false. Euclid, a mathematician in Alexandria in the fourth century BCE, included in his famous work, Elements, a discussion of mathematical statements that could be deemed “true” without actual proof, simply because their truth was obvious.