a treatise on Vectors, triangles, and directed simple paths
2:00 PM on Wednesday, December 16th, 2020 (Pasadena, CA)
Note from 2/8/2021: This entire write-up is kind of needless since its result is direct from the fact that the triangles in question begin and end at the same point! It’s funny how geometry becomes simple when you don’t think about it too hard. Regardless, I enjoyed this exercise and relating the topic to graph theory.
One course I’m looking forward to next semester is MA 362 Topics in Vector Calculus. I never really properly learned about vectors, and I wanted to get a sense of the topic before courses began, so I picked up a copy of Vector Calculus (Marsden, Tromba, 4th Edition) from ThriftBooks. I’m barely into it, but I’m already really enjoying the subject matter; it’s making me think I should revisit topics such as entry level physics and chemistry once more just for fun. Not to mention, the book has a really cool false-color photo of Comet Bennett on the cover, so how could it be bad? This morning, I came across the following example:
Nevermind that it is indeed from the first section of the first chapter of the book. . . everyone has to start somewhere! I was looking at this figure and noticed how the vectors v, w, and u formed a directed simple cycle. And that when these vectors are considered about the origin, they sum to zero. So, I did some Googling, but couldn’t quite find what I was looking for, so I wrote about it instead. My findings are given below; it ended up being somewhat of a ramble and a simple conclusion but I enjoyed learning how to make the figures in LaTeX all the same.
You can find the actual PDF by clicking here.
