Student to present Mathematics Seminar

GRCC student Steven Janke will speak on the historical development and fundamental concepts of Hyperbolic Geometry from 3-4 p.m. April 16 in room 103 of Cook. See below for the title and abstract.

For more than 2000 years, Euclidean Geometry was considered to be “the” Geometry; there were no others. The discovery of “new” geometries revolutionized mathematics in the 19th century. This talk should be of interest to the curious and open-minded, and, as always, all are welcome!

Pop and cookies will be served at 2:45 PM.

Triangles, Parallels, and Perpendiculars: A Story of Geometry

 One of the basic ideas in geometry is that when you add up all the angles in a triangle you get 180 degrees, but is this always true? Consider the earth and one line being the equator and two other lines being lines of longitude. If we pick two longitudinal lines that are perpendicular then these lines will form a triangle. However, this triangle has 3 right angles which add up to 270 degrees. Surely this must be a mistake, or some special case, or maybe there is something wrong with geometry…or could there possibly be alternative geometries?

Learn about the history of Hyperbolic Geometry, its creation and its discovery, and attempts to prove Euclid’s Parallel Postulate. Some of the major issues with newer geometries are finding logically consistent models, and we will explore some of the famous models for Hyperbolic Geometry and learn some of the basic constructions possible. We will finish with a qualitative investigation into curvature of a surface and what that means for geometry.

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