Tag: Geometry Page 4 of 7

How It Works

(Continued) J. H. Conway in 1971 discussed the role of an elementary abelian group of order 16 in the Mathieu group M24. His approach at that time was purely algebraic,…

The Uploading

(Continued) "Design is how it works." — Steve Jobs From a commercial test-prep firm in New York City— From the date of the above uploading— After 759 m759…

Mathieu Symmetry

The following may help show why R.T. Curtis calls his approach to sporadic groups symmetric  generation— (Click to enlarge.) Related material— Yesterday's Symmetric Generation Illustrated.

Symmetric Generation Illustrated

R.T. Curtis in a 1990 paper* discussed his method of "symmetric generation" of groups as applied to the Mathieu groups M 12 and M 24. See Finite Relativity…

Symmetric Generation

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity— From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)— "… we are saying…

Relativity Problem Revisited

A footnote was added to Finite Relativity— Background: Weyl on what he calls the relativity problem— "The relativity problem is one of central significance throughout geometry and algebra…

Alpha and Omega

A transcription— "Now suppose that α  is an element of order 23 in M 24 ; we number the points of Ω as the projective line ∞, 0,…

The Galois Tesseract (continued)

A post of September 1, The Galois Tesseract, noted that the interplay of algebraic and geometric properties within the 4×4 array that forms two-thirds of the Curtis Miracle…

How It Works

"Design is how it works." — Steven Jobs (See Symmetry and Design.) "By far the most important structure in design theory is the Steiner system S(5, 8, 24)."…

Design

"Design is how it works." — Steven Jobs (See yesterday's Symmetry.) Today's American Mathematical Society home page— Some related material— The above Rowley paragraph in context (click to…