Xah Math Blog Archive 2010-01
What's Function, What's Operator? (exposition)
Logical Operators, Truth Table, Unicode (thoughts; tutorial)
Added more symbols to Emacs: xah-math-input.el.
∅ 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 【⌥ option+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: 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 (For example, 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.
For why i created it, see: Design of Math Symbols Input System
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 firstname.lastname@example.org www.math.nus.edu.sg/aslaksen/ Symmetry and Patterns
- Trochoids: Curves Generated by a Rolling Circle By Christopher J Henrich. At http://userpages.monmouth.com/~chenrich/Trochoids/Trochoids.html. Links to:Visual Dictionary of Special Plane Curves.
- Home page of Davide Alessandro Reduzzi (Math 33A, lec. 3 to Linear Algebra and Applications) By Davide Alessandro Reduzzi. At http://www.math.ucla.edu/~devredu83/. Links to Conic Sections
See also: XahLee.org Site Awards and Recognition.
How Mathematica does Unicode? (tutorial)
Tools to Display Math on Web (tips)
some links to xahlee.org math:
- MATH 741: Spectral geometry of random metrics By Dmitry Jakobson. McGill University. Source www.math.mcgill.ca. Links to Visual Dictionary of Special Plane Curves.
- Math 214 - Differential Manifolds, Fall 2010 By Jonathan Dahl. UC Berkeley. Source math.berkeley.edu. Links to Gallery of Famous Surfaces
- Supplements to some chapters of Experiencing Geometry By David W Henderson. Cornell University. math.cornell.edu. Links to Inversion.
Principia Mathematica (random thoughts)
It's my greatest sorrow to have found that my friend Robby Villegas has died last month. Robby Villegas Died.
Math Typesetting, Mathematica, MathML (random thoughts)
Added a new section to bottom of: The Problems of Traditional Math Notation.
Gravity simulator (requires Adobe Flash). Source www.nowykurier.com
See also: Great Math Software.
For more info and where to buy, see: Geometric Pattern on Sphere and Torus.
See also: Math Symbols in Unicode.
If you are a emacs user, you can set your emacs up so that any frequently used symbols can be entered by a single shortcut key, or a abbreviation. See: Emacs and Unicode Tips.
Thanks to Tim Tran for Donation.
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Ian Stewart has a new book out.
- Professor Stewart's Cabinet of Mathematical Curiosities By Ian Stewart. Buy at amazon
Read 1/3 of his Flatterland Buy at amazon in ~2002.
See also: FLATLAND: A Romance of Many Dimensions, and Flatland: A Introduction (by Xah Lee) for many subsequent books and films on Flatland. It is one of my favorite book, say, in top 5, of all books in my life.
Thanks to R Michael Underwood for the tip.
Mathematicians Richard Palais and Hermann Karcher, have released a new version of their math visualization software, the 3DXM. The main change is that it now has button-like interface in place of menus, where each button is a icon of the surface or math subject. This makes it much more attractive, and easier to use. Check it out.
Download at 3DXM.
Note: the new version is for Mac only. For Windows or Linux users, there's always the Java version at the same download location. Though, the Java version has only some 50% of surfaces or other math objects.
A fantastic java applet to draw Voronoi diagram interactively. Very nice.
Voro Glide At www.pi6.fernuni-hagen.de…
See also: Great Math Software.
Math Prizes and Nobel Ignobility. (commentary)
My friend, Richard Palais, co-authored with his son Robert Palais a new book Differential Equations, Mechanics, and Computation. I've been hired to help them update the site. The result is this: ode-math.com. Half of the book is free in PDF files. Also, lots of java applets and animation files are coming.
You can buy the book at Amazon: Buy at amazon. However, for some reason, Amazon doesn't have extra copies.
Discovered that there are quite a lot articles in remembrance of Martin Gardner. See bottom of: Martin Gardner (1914 to 2010).
For more, see: Spirals in Nature.
Converting Math Problem Into a Question in Formal Language (Some thoughts)
In recent years, i learned quite a lot high powered mathematicians who are Chinese. Here's some list of Chinese mathematicians:
- Shiing-Shen Chern (陈省身) (born 1911)
- Hao Wang (王浩) (born 1921)
- Shing-Tung Yau (丘成桐) (born 1949)
- Chuu-Lian Terng (滕楚蓮) (b ~1960)
- Terence Tao (陶哲轩) (born 1975)
Wikipedia actually has a list: Category:Chinese mathematicians.
Chuu-Lian Terng is wife of Richard Palais. Richard i first met online in 1997, and them both in person in 2004, and has been personal friends since.
Here's some mathematicians that i admire. Typically, it more has to do with their subjects. Geometry, discrete math, combinatorics.
- H S M Coxeter (born 1907)
- Branko Grunbaum (born 1929)
- John Horton Conway (born 1937)
- Bill Gosper (born 1943)
- Stephen Wolfram (born 1959)
Stephen i met in 1995.
There are quite a few more but off-hand these comes to mind.
There are so many mathematicians today, that one hardly know much of them. Is there a list that lists the top one thousand mathematicians?
We chatted on Skype for about 40 min. He showed me, how my version of the proof on Sylvester-Gallai Theorem was wrong. Though, it's been 13 years since i wrote the proof, so, i couldn't seriously understand it without spending few days reviewing the stuff. Though, he convinced me he's right. I remember, when i was studying it, the proof given in the text seems a bit complex and convoluted, and i thought to myself that it should be done with a simple induction proof. After i did a proof, i wondered a bit why the problem went without a proof for some 40 years. This is back in 1996, and the internet only started, without all the blog and feedback and social networks, and i didn't put my notes online until 2004, and didn't show it to anyone.
He pointed out the Wikipedia article: Sylvester–Gallai theorem. That is a wealth of info.
Phlexicon also showed me a interesting elementary geometry problem. You might try to show it to your kids in highschool. Here's the problem:
Suppose there's a pyramid (as in Egyptian pyramid, with a square bottom), such that each of the triangle faces are Equilateral triangle. Let's call this pyramid p4. Now, let's say there's a regular tetrahedron, which is also a pyramid but with the base being a equilateral triangle. Let's call this p3. The question is, what is the ratio of volume of p3 and p4. (The length of the edge of p3 and p4 are the same.) You are to solve this problem by insight, and you are not allowed to use algebraic formulas.
Phlexicon said that this problem can be solved by insight, with 2 key realizations. I thought about it for 20 min yesterday but haven't seen it yet.
Cleaning up a blog a wrote few years ago: What is the Difference of Symbolic Logic System, Hilbert's Formalism, Russell's Logicism, Axiomatic System?.
Grigori Perelman and Money. (will you decline 1 million for some personal pride?)
Whether a single tile exists that tiles only aperiodically is a unsolved problem. This paper seems to solve it, or partially, this question.
See: An aperiodic hexagonal tile , By Joshua E S Socolar, Joan M. Taylor. arxiv.org 1003.4279v1.pdf
See also, some of my tiling studies:
- The Discontinuous Groups of Rotation and Translation in the Plane
- Plane Tiling Mathematica Package
- Tilings and Patterns
In the past few years, i discovered quite a few math formula editors that are not based on TeX/LaTeX. See bottom of: The TeX Pestilence (Why TeX/LaTeX Sucks).
Rudy is famous for his books such as “The Fourth Dimension” (1984), Infinity and the Mind (1995), and latest non-fiction on cellular automata: The Life Box, The Seshell, and The Soul (2005). Buy at amazon
The painting exhibition will be on from April 9 (Friday) to May 22 (Saturday), at Variety Preview Room in San Francisco. (582 Market Street, San Francisco, CA. (415) 781-3893) (View Map)
You're invited to an opening night party on Friday, April 9, from 6 to 9 pm.
In the closing event on Saturday May 22, from 6 to 10 pm, Rudy will read with author Michael Shea.
Paintings and prints will be for sale at the show during the opening and closing events, or online from Rudy's paintings page.
Wrote a little explanation on the status of my Visual Dictionary Of Special Plane Curves project. Here: Special Plane Curves: What's New.
Bird Flight V Formation (recreational math problem)
Discovered a fun math program (via mathpuzzle.com) called MagicTile. This software lets you play Rubik's cube but represented thru a Stereographic Projection. See: Great Software For 2D Visualization of Geometry.
In preparing to learn throughly about rotations, its representation, quaternions, computational techniques, i thought about what is a rotation? In a plane, you rotate thru a point. In 3D, you rotate around a axis. How about higher dimensions? What is the gist of rotation? A moment of thought leads to isometry with one invariant point, but that does not rule out Point reflection. Wikipedia has something to say about it Rotation (mathematics), will have to read later.
Learning Notes Of Symmetric Space and Differential Geometry Topics (learning notes)
Richard Palais and Bob Palais has some article about rotations for computer graphics, supposedly better than Quaternions. Here's the article: New Algorithms For Implementing And Interpolating Rotations , by Bob Palais and Richard Palais. transvection_for_rotations.pdf.
Bob also has some interactive demo written in Flash, here: Source www.math.utah.edu.
Fabrice Bellard, using a PC, Computed π to about 2.7 trillion places, claimed to be the latest world record. (previous records are made by super computers that costs millions.) He's home page is at http://bellard.org/, which details this among other things. A highly accomplished C programer. Probably the world's top 100 or even 10.
What's personally interesting is that he also created a Emacs-like editor: http://bellard.org/qemacs/. Undoubtedly he was a emacs user, but got frustrated with emacs's inherent inability of opening large files, or files with long lines, for dealing with π digits.
Am starting this math blog, of any thing that comes to my mind about math. This blog is branched off from my main blog Xah Lee's Blog, so it is more subject focused.
For ~500+ pages related to math on my website since 1997, see: Xah Math.
If you have a question, put $5 at patreon and message me.