Luca Crone of UIC : What is Hyperbolic Space?

Posted by Gregory Taylor , part of the MATH Club.

At

Oct. 14, 2026, noon

In

SEO 1227

Abstract

We all know the usual four axioms used in Euclidean geometry, namely; 1. A straight line can be drawn between any two points 2. Any straight-line segment can be extended indefinitely in a straight line 3. A circle can be drawn with any given radius and centre 4. All right angles are congruent However, Euclid had a 5th postulate, which can be simplified to the following: given one point, there is only one parallel line that can be drawn through it. The proof of the 5th perplexed mathematicians for 2,000 years and eventually led to non-Euclidean geometry, one of these being Hyperbolic Geometry.

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