Status of my Visual Dictionary of Special Plane Curves project
Perm url with updates: http://xahlee.org/SpecialPlaneCurves_dir/Intro_dir/whatsNew.html
The bulk of this project was done during 1994 to 1997. Minor updates are done after 2000, mostly updating the HTML format and adding GeoGebra applets. The total time spend after 1997 are perhaps about 4 or 5 months worth of man-hours.
The web has changed a lot since 1997, in format and style. Witness blogs, wikis, social networks, and in particular Wikipedia. Also, i haven't been spending much time on this project since.
The Mathematica code on this site was written for Mathematica version 3. Today, Mathematica is at version 8, and I do not have it. (code should still be compatible, however.)
The project's format and style was originally intended to be more close to a book, with printed publication in the works. However, i did not follow through.
In the past few years, i've been wanting to update this project with Differential Geometry and Algebra Geometry foundations and proofs. There are several personal obstacles:
- My understanding of differential and algebraic geometries are at beginning level. So writing about them will be a learning process.
- The traditional math notation is extremely bad. I refuse to use it. (See: The Problems of Traditional Math Notation.)
- The technology for showing math notation on the web is still pratically none-existant. Pratically, you either resort to images or ask user to install browser plug-ins. In particular, i do not wish to use images for formulas, nor anything based on TeX. (See: The TeX Pestilence.)
- I'm not happy with the traditional foundation of mathematics and proofs. I'm more interested in computerized proofs.
- Differential and algebraic geometries are rather different subjects. At least at the undergraduate level, they cannot be mixed up as a coherent foundation. For example, a plane curve is defined totally differently in differential geometry and algebraic geometry. It's hard to use them both together as a coherent whole, but i do wish somehow to treat curves in this project using both approaches as foundation and technique. The only way i see how this might be solved is by defining curves as computational entities. e.g. curves somewhat defined like signal processing, or probabalistic model on numerical computation...
For the above reasons, the plan for this project changed to using Theorem Proving Systems. The notation would be more or less be computer language source code. That would mostly solve the above problems for me, personally. This means, i started to learn the OCaml language, but in short, the task according to my plan is rather big and it did not really even begin.
Given the above reasons, i'll just say that this project now remain dormant, as a matter of fact. For readers who are interested in my math dabbling, please subscribe to my Math Blog.