Hello fellow members of the Math Department! Jon and I worked on our 381 talk together on Taxicab Geometry. In our talk we will touch on the basics of Taxicab Geometry to get a good understanding, then get into the distance formula used and a look into n-dimensional Taxicab Geometry. Hope you guys enjoy it and hope you are all staying safe!

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Great presentation. I like how you both compared taxi-cab and euclidean geometry, with examples. It is an easy presentation to follow and well organized. You could have condensed a few of the slides with \begin{itemize}, \item, then \end{itemize}, which I saw you start to do in the last two slides. This will help organize it a little better. There is also a function in latex \newtheorem{theorem}[Theorem] that you can use for your theorems and \newtheorem{defin}[Definiton] which you can use for definitions. This also helps better organize the presentation for the future. Overall it was very good and an interesting topic to read about. You both did a great job!

Overall it was solid. I liked how the focal point of the presentation was about understanding how this geometry is just fundamentally a style of geometry based on measuring the components of a vector rather than traditional euclidean where the measurement is along the resultant. Also dynamite job of expanding this to n-dimensions. Understanding 2-dimensional TCG made expanding to three dimensional and n-dimensional very easy. Both of you seem to have great knowledge of this subject, must have had really good references and sources. (Per Dr. Kinsey’s citation)

Very well done and formatted! My personal favorite was learning about sin(x) and cos(x) within taxicab geometry. I’m interested to see if there’s any avenues for further research in this area, although I don’t know what it would be applied to. Great job!

I thought this was a phenomenal presentation. It flowed very nicely, the questions I came up with were answer in nearly the next slide. Additionally, the examples provided made it very easy to understand the fundamental differences between the Euclidean and taxicab geometries. Great job!

Great job! I really like how you would explain these concepts not only mathematically by using the formulas, but you then put it into words and to get at the logical side of it, too. It’s always really helpful for me when trying to learn something new to understand why the formula works the way that it works, which you guys did really well.

This was a very nice presentation! Walking thought the counterexample was very helpful and thank you for showing all of the steps as it made it easier to follow along. I thought about how dispatch centers send emergency services to a location. I wonder if they rely on euclidean distance for more rural areas and taxicab geometry for more urban places? If they measured in taxicab geometry with the density of traffic as a conditional factor could they be able to dispatch emergency services faster? This was just the thought I had when you mentioned Uber and our phone’s GPS utilizing taxicab geometry.

Hello! I think that your presentation is absolutely amazing! You both did an excellent job of taking information and then summarizing it and explaining it in a way that someone like me could understand. It made reading through your presentation very enjoyable since you made everything so clear to follow. Also, I found your topic super interesting. I’m not taking geometry until next semester, so I really loved this taste of upper level geometry! Awesome job to both of you for making such a cool and enjoyable presentation!

Great job guys! You put a ton of work into this and it came out really well. By far the BEST presentation I’ve ever seen in my entire life. A+++++

That’s interesting topic! Since I studied euclidean geometry, I didn’t wonder something like Taxicab Geometry. It is new concept to me. I enjoyed and felt like upper level geometry. Great job!

Super neat! I always enjoyed doing physics because vector math was so nicely decomposable into components. It’s intriguing the implications that this non-euclidian system of measurement has on the distances; I’m sure this is super applicable to GPS navigation given that we can almost never travel from point A to point B in the straight line path, we always have to decompose the components into little cardinal-direction sections.

Very creative topic choice and super digestible!

Great presentation. I find it really impressive that you were both able to work together on this given the circumstances. Your presentation was so well put together. I really liked that you guys compared taxicab geometry with Euclidean geometry since that is what we are used to. The comparison really gave me a better understanding on what taxicab geometry does.