November 30, 2005
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For St. Andrew’s Day
“The miraculous enters….
When we investigate these problems, some fantastic things happen….”– John H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, preface to first edition (1988)
The remarkable
Mathieu group M24, a group of permutations on 24 elements, may be
studied by picturing its action on three interchangeable 8-element
“octads,” as
in the “Miracle Octad Generator” of R. T. Curtis.A picture of the Miracle Octad Generator, with my comments, is available online.
Related material:
Mathematics and Narrative.
