Published on: February 24, 2013
Vectors with negative magnitude. Tractricoids and pseudospheres. Quarternion hyperboloid geometries. These are just a few of the many phrases given by Ilesanmi Adeboye, an assistant professor from Wesleyan University during his talk on Tuesday, Feb. 12.
Adeboye began the talk by presenting five basic ideas that play major roles in Euclidean geometry, four of which are important axioms. He then discussed how the fifth idea, the parallel postulate, is not necessarily true in other non-Euclidean geometries. Continuing along the lines of this thought, Adeboye demonstrated how a triangle drawn on a sphere can have an interior angle sum of 270 degrees, a concept which seems to break all the rules of Euclidean geometry.
Luckily, it was not Euclidean geometry. After inspecting this concept for certain by utilizing a spherical fruit as a helpful demonstration tool, and by mentioning how this same concept relates to the distortion visible on any map, Adeboye then brought up hyperboloid geometry. The primary focus was a hyperboloid in two sheets, and how the mapping of the hyperboloid related to the mapping of one unit cell in Euclidean geometry becoming what looks like a donut, though mathematics prefers the term torus.
Overall, Adeboye’s talk was highly informative about many concepts accessible to any student having completed Calculus I and II. Adeboye successfully incorporated humor throughout his presentation as many chuckles could be heard from the audience. He also brought out real-world applications of the presented concepts by relating topology to M.C. Escher’s art and many other geometries that commonly incorporate non-Euclidean geometries.