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.
Random Notes On Nicolas Bourbaki. (reading notes)
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 (2008-03-21), by Bob Palais and Richard Palais. transvection_for_rotations.pdf.
Bob also has some interactive demo written in Flash, here: http://www.math.utah.edu/~palais/transvection.html.
My friend, professor Richard Palais, co-authored with his son a new book “Differential Equations, Mechanics, and Computation”. There's a website for it: http://vmm.math.uci.edu/odeandcm/. The site is still in the works.
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.
His other accomplishments include: FFmpeg (for processing multimedia data (e.g. audion and video)), QEMU (cpu emulator).
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 published on my website(s) since 1997, see: XahLee.org Site Math Index