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!

For what it is worth, after all the energy changes between now and when you gave the presentation about 2 week ago based on a calendar system used during on the date 4/29/2021; The thing that stood out the most to me and has stuck with me the most is the illustration of how the poinecare-disc model is projected from 2D model of the circle to a 3D one, using a sphere. I have had some struggles obtaining complete understanding of this model and these presentation did a good job and helping me push much closer to that point of teachability. Thank you for your service.

Great job on the presentation! Although, I am not a big fan of Geometry especially with Euclidean geometry and Hyperbolic geometry. It was a good learning experience since I get know about Beltrami-Klein and Poincare Disc Model. Well-organized and thoughtful presentation. It made me easier to understand more when you show me the graphs on slides. Thank you for the presentation. Looking forward to your future research.

Great job on your presentation. I found it really interesting because it touched upon some of the topics that we didn’t get to in the geometry course. It was easy for me to stay caught up with what you were saying because I took the geometry course, but with your clear explanations, even someone who didn’t take the geometry course could still keep up.