Math IA

• I was told that I got a top score.
  • I feel pretty amazing that I was able to get a good grade (apparently) on my pure math IA that I started working on seriously a week before the deadline.

In the end, on 20210615, I decided to go with Generalization of Euler’s Form for Complex Numbers.

• On 20210513, I need to make a decision soon, so I temporarily abandoned the idea of Generalization of Euler’s Form for Complex Numbers and brainstormed other topics.

  • Anagram
    • Creating mathematical anagrams, for example.
  • Attraction Phenomenon/Kuramoto Model
    • It could be an interesting topic if I develop Elastic Synchronization mathematically.
    • Kineto’s elastic synchronization algorithm
    • Since I didn’t know about derivatives at that time, it might become even more interesting if I revisit it now.
    • It would be fascinating to incorporate the concept of Feedback from Cybernetics.
    • Distorted time, two-axis time, and attraction phenomena.
      • Generalizing for that purpose, perhaps.
    • https://twitter.com/etiennejcb/status/1393295149493522435?s=20
      • I want to create a cool GIF (maybe).
    • → Math IA on the Coanda Effect
  • Mastering Information Science: Image Processing Research
    • This might become too focused on information.
    • If it involves processing each pixel of an image, it could still be suitable for a Math IA to some extent.
  • Game of Life, Cellular Automaton
  • Finding shortest paths in non-Euclidean spaces (spaces distorted by quadratic functions), for example.
  • The fog of the world
    • How many times do we need to fill all the grids?
      • We want to minimize the average distance.

• It would be interesting to have something that can be experimented with in a program.

• Although it was helpful for gathering ideas, Mathematical Girl was probably not suitable for a Math IA because it focused more on exploring mathematics itself rather than modeling.

  • It was good for brainstorming, though.

• I want to try modeling something from the real world as a new mathematics, like V_Melville’s color or seasonal models.

  • n-color Function

• Generalization of Euler’s Form for Complex Numbers

  • Maybe I should go with this.
  • I can’t see much expansion potential, though.

• Something involving Complex Numbers for modeling.

• If possible, something related to time (t).

• High scores:

  • 18 https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=12&mode=moderator
  • 16 https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=4&mode=moderator
  • 16 https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=20&mode=moderator
  • 16 https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=2&chapter=22&mode=moderator

• Places where I might find interesting topics:

  • http://shochandas.xsrv.jp/toukou.htm
  • /sansu-programming