I’m working on developing a 3-D convex hull algorithm in Mathematica for the 4-colour rhombohedral lattice. Right now I’m trying to grasp how to store the connectness or topology of the convex shell.
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Tesseract and the 4-colour Rhombohedral Lattice
I’m fairly sure that the 4-colour rhombohedral lattice contains the tesseract. A Google search for tesseract images led me to the following very interesting web page:
http://members.shaw.ca/johnhendricksmath/tesseracts.htm
Wald Papers
I came across a very interesting paper entitled The Thermodynamics of Black Holes by Robert M. Wald, 2001, at the following link:
http://relativity.livingreviews.org/Articles/lrr-2001-6/
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Kissing Number
I found a great link this morning on Mathworld.com, a piece about the Kissing number. This is twelve in 3-D and 24 in 4-D. I wonder if I can explain 24 for 4-D on the four colour rhombohedral lattice.
http://mathworld.wolfram.com/KissingNumber.html
Creating TeX Fonts
I came across a new web site today that looks like it may help to resolve some of the difficulties in creating AblBeebl for TeX.
http://www.radamir.com/tex/ttf-tex.htm
Some of my Efforts to Understand Group Theory
Group theory is the mathematics of symmetry and Mark Ronan’s book “Symmetry and the Monster” has greatly helped me to learn and understand the fundamentals of group theory and especially simple finite groups.
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FGB Program for Learning Group Theory
I came across this great web site today after working through some notes I had found on-line by Blake Stacey about Group Theory. FGB stands for Finite Group Behaviour and is a Windows 98 program. I have downloaded the program and associated documentation to try it. It looks very promising indeed as a learning aid. After checking it out I will register, as requested by sending my contact details to Dr. Keppelmann.
http://wolfweb.unr.edu/homepage/keppelma/fgb.html
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Creating TeX AblBeebl fonts
The procedure followed for creating the Ablbeebl font for use in LaTeX (Ubunto distribution of Linux, TeX Live) is given below.
- Create .pfb files for each character set of AblBeebl using FontForge. Place these in a working folder (e.g. AblBeebl_r006) in the Home directory. There are two font faces AblBeebl Serif and AblBeel Sans. For each font face there are four character sets: Regular (the default face), Italic, Bold and Bold Italic. Adobe Standard Encoding is used. Only the upper and lower case letters are contained in each character set. The file names are ABLSR, ABLSRBD, ABLSRBI, ABLSRI, ABLSS, ABLSSBD, ABLSSBI, ABLSSI.
AblBeebl Project Status
AblBeebl sample font
Sustainability – a Contrary View
I have always been in favour of efficiency and the avoidance of waste. As an engineer much of my career has been devoted to the development of better systems for using energy. I am currently a member of the Sustainability Group at the Dublin Institute of Technology. I am not a member of the Green Party or Greenpeace or any such organisation, although I respect their positions and am glad that they exist. By the way, the views expressed here are entirely my own; in fact they are not so much views as reflections, because I am not secure or at ease with them, and they are not static.
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