Xah's Math Blog

2011-06-27

M C Escher Stars chameleon by Wizard Gynoid

Art: M C Escher “Stars” Chameleon Polyhedron.

2011-05-20

Updated my Mathematica package for plotting Geometric Transformation ＆ Complex Function.

Get it at: Mathematica Package: Geometric Transformation ＆ Complex Function Plot

2011-04-20

Geometry: Ellipses, Linkages, and Solids of Constant Width. (video)

2011-03-25

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

2011-03-22

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

2011-03-15

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

2011-03-13

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

2011-02-24

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

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

2011-02-14

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

2011-02-07

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.

2011-02-03

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

2011-02-03

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).

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2011-01-27

Looks like a great out of print book Tiling and Patterns (1986) 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.

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2011-01-23

combinatorics and space-filling curves

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 combinatoric 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.)

Possible loops with 5 points:

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.

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2011-01-20

Mathematica Version 3 to Version 7 Conversion Notes

2011-01-18

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

2011-01-07

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

2010-12-30

Turning a torus inside out.

2010-12-27

Math Politics: Simon Plouffe and nth Digit Formula of π

2010-12-15

What's Function, What's Operator? (exposition)

2010-12-14

Logical Operators, Truth Table, Unicode (thoughts; tutorial)

2010-12-13

Added more symbols to Emacs Math Symbols Input Mode (xmsi-mode).

∅ ƒ Ø ⌘ ⌥ ‸ ⇞ ⇟ ↖ ↘ ⌫ ⌦ ⎋ ⏏ ↶ ↷ ⇧ ⌤ ⇄ ⇤ ⇥ ↹ ↵ ↩ ⏎ ⌧ ⌨ ␣ ⌶ ⎗ ⎘ ⎙ ⌚ ⌛ ✂ ✄ ✉ ✍ □ ○ ◇ ■ ● ◆.

The symbol “ƒ” has unicode name “LATIN SMALL LETTER F WITH HOOK”, and its old unicode name is “LATIN SMALL LETTER SCRIPT F”.

It's a popular symbol on the mac in the 1990s. Often, a folder's name will end with it. You can type it on the Mac by pressing 【⌥ Opt+f】 See: Mac OS Roman. In math, that symbol is sometimes used to stand for “function”.

Many other symbols above are computer key symbols. They are used by Apple. (See: A Short Survey Of Keyboard Shortcut Notations)

◀ ▶ ▲ ▼ ◁ ▷ △ ▽ ☉ ☼ ☾ ☽ ☿ ♁ ♄ ♅ ♆ ♇ ♃ ♂ ♀ ☄

The symbols includes the 9 planets. Note that in Unicode the ♂ (unicode name MALE SIGN) and ♀ (FEMALE SIGN) is the same symbol for Mars and Venus. Unicode does not have separate char for them.

Also some interesting readings. See: Astronomical symbol.

Also, discovered this article about the pseudo-science book Worlds in Collision, which was a best-seller in 1950s. But today's people probably all forgot about it. By analogy, you should know that many concepts, ideas, practices, we have today in math, sciences, in programing, are probably garbage. In particular, i could personal say this is so with regards to math notations, computer syntaxes, and many computing practices (e.g. Design Patterns, eXtreme Programing, which were hot in early 2000s but today pretty much waned. See: Why Software Suck) See also: Men Are From Mars, Women Are From Venus.

Also added the del operator Nabla symbol ∇. The partial derivative symbol ∂.

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2010-12-12

If you use Emacs and type a lot math symbols, you may be happy to note that i wrote tool for inputting math symbols. See: Emacs Math Symbols Input Mode (xmsi-mode). For why i created it, see: Designing a Math Symbols Input System.

2010-12-12

Math Font, Unicode, Gothic Letters, Double Struck.

2010-12-07

Discovered another citation to my Wallpaper groups: The 17 Wallpaper Groups work.

Chapter 1 Symmetry Groups
Mathematics in Art and Architecture GEK1518
Helmer Aslaksen
Department of Mathematics
National University of Singapore
aslaksen@math.nus.edu.sg
www.math.nus.edu.sg/aslaksen/
Symmetry and Patterns

At Source www.math.nus.edu.sg.

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