Hi everyone! My name is Kara Paradowski and I will be giving my 480 presentation on Wednesday April 7, 2021 at 2:10 PM via zoom. I hope you all can attend! Here is a quick description of what I am going to cover in my talk.

There are many types of geometry that we study, and one that we briefly talked about was hyperbolic geometry. So, I am going to dive more into that, more specifically, distance in hyperbolic geometry.

Prior knowledge on geometry is not needed but may be helpful. I’ll touch on main points of hyperbolic geometry to catch you up to speed, then I’ll go over important models that play a role into finding the distance, the formulas, (yes, there are multiple), and then calculate the distance by using one of them.

Objectives:

- Understand similarities and differences between Euclidean and Hyperbolic Geometry
- Learn about the history of hyperbolic geometry
- Learn about the Beltrami-Klein and Poincare Disc Model
- Learn about finding distance in hyperbolic geometry

Hope to see everyone Wednesday!

Okay first of all, great job. Second, that graphic on slide 11 would have changed my life about 6 months ago when we were in Geometry. I had absolutely no idea that that is how the model was derived. This was super interesting. Love hyperbolic geometry. Anything non-Euclidean just blows my mind wide open, as I’m sure it does with everyone else. It’s so counter-instinctual to think that even something as simple as distance can be difficult to measure in other geometries.

Hi Kara! Great job on your presentation! Considering that there is an entire course in Geometry, you did an amazing job of getting everyone up to speed! Your explanation of the differences between Euclidean geometry and Hyperbolic geometry was very helpful to those who haven’t taken Geometry, but also to those who have taken Geometry but just needed a refresher on some key points. I really liked that you included images as to how the Poincare-Disc Model and Beltrami-Klein Model were developed and work. Those graphics were super helpful! Great job on all of those proofs too! Overall, your presentation was very informative and interesting! Great job!