I have written a little story called ‘Lost Overground’ that could also be about geometry, courage, non-random-walks, cyclic activities, fate, gardening, or day-dreaming on a job. Perhaps it’s a technical report about a trivial incident, or a visualization problem for a student to solve. Is it an incredible tale? Make of it what you will.

# Category Archives: Mathematics

# 3-D Convex Hull

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

# 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

# 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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# Classic 1908 Book on Groups of Finite Order by Harold Hilton

This book is available on-line from the Cornell University Library Digital Collections:

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# Symmetry and the Monster by Mark Ronan, 2006

This book has been an enthralling and fascinating read for me. Mark Ronan outlines the mathematics of symmetry and details its historical development from Evariste Galois’s letter of May 1832 to about 2005.

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