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Friday, February 25, 2011

Diamond Theorem Exposition

Filed under: General,Geometry — m759 @ 11:00 PM

"THE DIAMOND THEOREM AND QUILT PATTERNS
Victoria Blumen, Mathematics, Junior, Benedictine University
Tim Comar, Benedictine University
Mathematics
Secondary Source Research
 
Let D be a 4 by 4 block quilt shape, where each of the 16 square blocks is consists of [sic ] two triangles, one of which is colored red and the other of which is colored blue.  Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D.  The diamond theorem states that G(D) = D_g has either ordinary or color-interchange symmetry.  In this talk, we will prove the diamond theorem and explore symmetries of quilt patterns of the form G(D)."

Exercise Correct the above statement of the theorem.

Background— This is from a Google search result at about 10:55 PM ET Feb. 25, 2011—

[DOC] THE DIAMOND THEOREM AND QUILT PATTERNS – acca.elmhurst.edu
File Format: Microsoft Word – 14 hours ago –
Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D. The diamond theorem states that G(D) = D_g has either
acca.elmhurst.edu/…/victoria_blumen9607_
THE%20DIAMOND%20THEOREM%20AND%20QUILT%20PATTERNS…

The document is from a list of mathematics abstracts for the annual student symposium of the ACCA (Associated Colleges of the Chicago Area) held on April 10, 2010.

Update of Feb. 26For a related remark quoted here  on the date of the student symposium, see Geometry for Generations.

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