Discovered a Unicode math symbol that's from Mathematica: “⧴” (RULE-DELAYED). Are there others? (see: Math Symbols in Unicode.)

Update: interactive GeoGebra applet showing Product of Rotations, at Product of Rotations.

Fixed the java certificate problem. Now it works in all browsers: 60+ GeoGebra Files for Plane Curves.

60+ interactive geometry GeoGebra apps for Plane Curves at: Plane Curves: GeoGebra Files Index.

Reminder. If you like this blog, you might also enjoy my other programer related blogs:

- Xah Programing Blog, subscribe here
- Xah Emacs Blog, subscribe here
- Xah Web Dev Blog, subscribe here
- Xah Math Blog, subscribe here

Usually i don't repeat a article in more than one place, even if it's related to both.

Xah's edu corner: How Long is One Year?

There's a extremely simple, nice, web site for creating math notations then you can point a URL to. You type LaTeX code, it displays the results as a image on-the-fly immediately as you edit. It also comes with a short perm URL that you can point to. You can come back to the URL later and edit the expression anytime. The site is at mathurl.com

added to: Tools to Display Math on Web.

Mandelbrot Set Explained (no complex number needed) (with youtube video)

Google made a fractal application, based on Google Maps, at juliamap.googlelabs.com.

Though, am rather disappointed. When you zoom in just a few steps, the resolution does not automatically increase enough to get crispy edges.

Much better are some dedicated fractal apps. See: Great Fractal Software.

For a basic explanation of the mandelbrot set, see: Mandelbrot Set Explained (no complex number needed).

Looks like a great out of print book Tiling and Patterns By Branko Grunbaüm and G C Shaphard, is being republished by Dover. amazon

I'd say this is best math book i've ever read. (technically, i'd put this book in one of the top 10 i've read, because there are quite a lot good math books on various topics and written with different style for different audiences.)

below is some very old articles i wrote, about the book and other math books.

I worked intensively on tilings for about a year in around ≈1997. The most mathematical is: The Discontinuous Groups of Rotation and Translation in the Plane, which are linked a lot. It is basically my own learning notes. All images are generated by Mathematica, a package i wrote: Plane Tiling Mathematica Package. I'll be updating it from Mathematica v3 to v7 in next few days. At the time, i wanted to create a most versatile software that generates any type of tilings, decorative patterns, without human intervention. A sort of AI in the spirit of Douglas Hofstadter. (See: Gödel, Escher, Bach amazon) Of course, i didn't get that far. For gallery, see: Geometric Tilings and Patterns Image Gallery.

All these pages are written in late 1990s. Much update needs to be done, on the html and the writing too.

Robert Dickau has done many nice combinatorial diagrams with Mathematica. For example, here's some i like:

- Bell Numbers @ http://robertdickau.com/bell.html
- All Self-Avoiding Paths Through a Lattice @ http://robertdickau.com/allpaths.html
- Stamp Folding @ http://robertdickau.com/stampfolding.html

His home page robertdickau.com has many more. You can also get many of his interactive Mathematica files at demonstrations.wolfram.com.

You might also enjoy a combinatorics diagram i did. See: Number Of Ways To Loop n Points. (it was done with Mathematica v3. I'll update the notebook to v7 soon.)

Many of Robert's work are about space filling curves. It is one of the math i learned in early 1990s that had a big effect on me. In short, it shows that there are same number of points of one side of a square to the square itself. At the time, it was a shock to mathematicians. See: Space-filling curve, and Xah's Top 10 Math Wonders.

Mathematica Version 3 to Version 7 Conversion Notes

3D Visualization Design (wolfram demo project; commentary; tips)

What's the Latest and Greatest in Calculators? (musings)