Project Ideas
1 Project Ideas
- Taxicab Project
- Investigate the taxicab metric in more detail, see Section 3.2.
- Image Creation
- Draw digital images for use in the notes.
- Euclidean Constructions
- Use a software package to construct proofs. Some geometry software:
- Regular Polygons and Tiling
- Investigate tilings of the plane, see Section 4.4. See also the wikipages (more involved projects):
- Fractals
- Investigate fractals, see the end of Section 4.6.
- Area and Volume
- Investigate area and volume, from Euclid's point of view, see Section 4.6.
- Lecture Notes
- Create lecture notes for high school geometry, see Appendix B.
- Quaternions
- We extend the reals to get complex numbers. We extend the complex numbers to get the quaternions, we extend the quaternions to get the octonians. This project is to investigate the quaternions. See https://www.youtube.com/watch?v=d4EgbgTm0Bg.
- Geometric times tables
- Investigate/create something like https://www.youtube.com/watch?v=qhbuKbxJsk8.
- Toothpick patterns
- A project about toothpicks. See https://www.youtube.com/watch?v=_UtCli1SgjI and http://oeis.org/A139250/a139250.anim.html.
- Turtle graphics
- Use a programming language to make some nice pictures. Google "logo programming" or "turtle graphics". See https://mathnotes.cc/research/applied-topology/turtle-geometry/turtle-graphics/index.html.
- Turtle Polynomials
- Related to turtle graphics, but solve polynomials. See https://www.youtube.com/watch?v=IUC-8P0zXe8.
- L Systems
- Similar to turtle graphics, useful in modeling biological systems. See https://en.wikipedia.org/wiki/L-system.
- Other
- If you have another idea, then talk with me.