What is New

Get the CD-ROM .

The site is currently under heavy reworking. All Mathematica notebook lines are dead. Will be fixed this weekend.

Mathematica 8 is released.

I got Mathematica 7 this month, as a gift from Wolfram Research. (before they released 8) (Thanks Wolfram) I haven't actively been coding Mathematica since about 2000. In the coming months, i'll update my tens of Mathematica packages on my site to Mathematica 7.

Mathematica started in 1988 as a so-called computer algebra system. Namely, it lets you do things like solve equations, factor polynomials, do integration, derivative, etc. But, due to Stephen's design, it is also a full featured general programing language, much based on lisp. (he probably would not admit it) But since about late 1990s, Mathematica is more marketed as a technical computing platfrom, a system for doing any technical computation. The reason is simple: because as a math system, the market is very limited, but as a system for any technical computation, it widens its potential audience by some 10 fold or 100. Since ~2005, it became increasingly more broad. Although i haven't actively been coding Mathematica, but some quick look at Mathematica 7, it is really fantastic. Dynamic visualization, data center of all technical info, and this year [ Wolfram Alpha ] [ https://en.wikipedia.org/wiki/Wolfram_Alpha ] .

Here's things i've done with Mathematica, all or almost all graphics in the following projects are generated by Mathematica version 3 (~1998) or 4 (~2002):

In the coming months, i'll be completely revamping this curves site. Update all Mathematica files to version 7, and probably will update all content, and those QuickTime movies files to something more modern.

You can buy Whole Site as a download. When i have update, you get free update for a year.


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 6 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 Algebric Geometry foundations and proofs. There are several personal obstacles:

For the above reasons, the plan for this project changed to using Theorem Proving Systems. The notation would be more or less programing language source code of a theorem proving system. 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. If you are interested in my math dabbling, subscribe at Math Blog .


GeoGebra used on this site has been updated to the latest version, 3.2. For a feature list of GeoGebra 3.2, see: Release Notes GeoGebra 3.2 .


Spent about 6 hours converting HTML 4 Transitional to HTML 4 Strict for my Visual Dictionary of Special Plane Curves website. There are 410 HTML pages. Note that all HTML pages are valid HTML (i.e. passes W3C's HTML validator), both before and after. Even with valid HTML, the trasition is not trivial. The trasition are done semi-manually with emacs. (in particular, using its feature of Interactively Find Replace String Patterns on Multiple Files)

Besides convertion to HTML 4 strict, i also took time to clean up the pages. In particular, change various HTML formatting to be some consistent canonical form. And, change the HTML tag use so that their semantics can be mechanically parsed. This is to pave the way for [ semantic web ] [ https://en.wikipedia.org/wiki/semantic_web ], and perhaps in 2009, i'll transform the site again to xhtml. The goal is that, the site can be easily transformed to any other format such as PDF or others for book publishing, by mechanical means, and without losing any info or manually diddling with display formatting again.

Almost all the changes are changes of appearances or formatting. There is not much content or math additions.


Here's some description of the changes for those technically curious:

Changes For Html 4 Strict or XHTML

Semantic Formatting Changes

Misc changes

To Do



Archimedean spiral

Inversion of Archimedes's spiral

Real Rose Curve

Peaucellier Linkage on a line

Thales's Theorem

Converse of Thales's Theorem

Archimedes Circle

Inversion of A Line

Inversion of A Circle

Inversion of Sine Curve

Uploaded about 170 scanned pages of the book by Yates, here: “Curves And Their Properties” by Robert Yates. Please support this website by making a donation or buy a downloadable version.

The site is now heavily linked to Wikipedia. Mathematician's names in the history section are linked to Wikipedia, and any other theorem or relevant fact appeared in this site's text but not explained, are linked to Wikipedia. Also, every curve page now has a link to Wikipedia's entry at the bottom.

Dead links or links to college student's works are removed.


Spent a couple hours and updated the Plane Curves Books page. With links to Wikipedia and amazon.

Figure 8 Curve

Adde material to Cornu Spirals .

Cornu Spirals .

Still in the process of phasing out Geometer's Sketchpad files on the site. There are like 120 of them. Eventually, they should all be in one single zip file for download. Geometer's Sketchpad is replaced by GeoGebra.

Tractrix Tracing

Sine Curve

Updated the page: Naming and Classification of Curves .


Update: Math of Seashell Shapes .

Equiangular Spiral Evolute

Equiangular Spiral Caustic

Equiangular Spiral

Parabola Point Tangent Construction

Deltoid Caustics

Tracing a Parabola

Parabola Caustics

Cardioid As Circle's Caustics

ball shadow
A computer generated rendering of ball shadow added to conicSections page.

Several new Geogebra files added:

Cardioid Tracing

Several construction's proofs added to ellipse page.

Hyperboda Point-wise Construction


Added many Geogebra constructions to the conic sections page:

For older update news, see: Special Plane Curves: What's New 1996 to 2007 .