My Favorite Theorem

After listening to the podcast of my favorite theorem with Dr. Candice Price, I am happy to say that her theorem has been one of my favorite concepts of this course. I love how we are able to find a rational number given a tangle and how we are able to sketch a tangle given a number. In their discussion, Dr. Price explained a tangle as webbing inside of a ball. This reminded me of what we did with the ropes inside the envelope. Even though we have discussed this in class, I think introducing the rational tangle dance to the younger students will give them a different perspective on math, add some excitement behind how “math” can be applied. Especially since fractions are so “scary” to all students K-12, showing them that they have applications and are not that scary could make them excited to use fractions in the rest of their math career. 

At the end of the podcast, they talked about how to pair the theorem with something "real". I think that this is a great idea and brings life to these concepts. Dr. Price said that she would pair her favorite theorem with a Neopolitan Shake: three different flavors--> chocolate, vanilla and strawberry all equally interesting just like Rational Numbers, DNA and topology and when they are all mixed together they create a wonderful combination. 

Some new aspects of rational tangles that Dr. Price brought up was how rational tangles show up in DNA topology. DNA are long thin strands that wrap around their selves creating rational tangles. This allows scientists to use what they know about rational tangles and apply this to DNA.

Some questions that surfaced for me was the concept of non-rational tangles and how they are classified into prime and locally knotted. I think we have talked about this before briefly in class, but I couldn’t find the video for more information. From what I listened to the prime tangles were similar to what we discussed with Dowker. I would love to have more information or even visuals of what non-rational tangles looked like and is it ok to say “irrational”?

I know this is something that we are going to talk about in class and work on but I feel very passionate about introducing the concept of rational tangles to younger students. I would like learn how to accurately and confidently explain the concept of rational tangles to my high school students. Also I would like to make sure I find a way to bring rational tangles to a level where my students can understand and not feel intimidated. Something else that would be beneficial in explaining this to our students would be to come up with a resource that they can go back to reference when needed. 

Ka

I found that the paper by Tanton and the paper by Kauffman and Lambropoulou have the same Theorem 1 about isotopy. Kauffman and Lambropoulou's discussion on theorem 1 is lengthy and without any diagrams. Tanton's explanation is direct and to the point.

I found it very difficult to read Kauffman and Lambropoulou's paper. It was very wordy and detailed. As much as I love math and find it extremely interesting but I am not a fan of reading papers like this. It takes me a while to read and if I want to absorb the information, I need to read and re-read each part. So with their paper it took a very long time for me to get through it. And to be honest, I am not sure if I understand it fully yet. On the bright side, I really like their diagrams and drawings. I found those easy to understand and useful.

I think Tanton's paper is easier to understand and more reader friendly. I found it helpful to break up definitions and explanations with diagrams. It allowed for us readers to digest what we just read.

I believe that the audiences for both of these papers are fairly similar. I think that audience for Tanton's paper is grad school students who might not have much experience with  reading though papers or dealing with difficult concepts. I think Kauffman and Lambropoulou's paper is more for teachers and professors looking to dive deeper into the concept. Maybe readers with a background in the content area.