Saturday, March 17, 2012

The Purloined Diamond

Filed under: General,Geometry — Tags: , , — m759 @ 12:00 PM


The diamond from the Chi-rho page
of the Book of Kells —

The diamond at the center of Euclid's
Proposition I, according to James Joyce
(i.e., the Diamond in the Mandorla) —

Geometry lesson: the vesica piscis in Finnegans Wake

The Diamond in the Football


“He pointed at the football
  on his desk. ‘There it is.’”
         – Glory Road

Wednesday, December 21, 2011

The Purloined Diamond

Filed under: General — Tags: , — m759 @ 9:48 AM

Stephen Rachman on "The Purloined Letter"

"Poe’s tale established the modern paradigm (which, as it happens, Dashiell Hammett and John Huston followed) of the hermetically sealed fiction of cross and double-cross in which spirited antagonists pursue a prized artifact of dubious or uncertain value."

For one such artifact, the diamond rhombus formed by two equilateral triangles, see Osserman in this journal.

Some background on the artifact is given by John T. Irwin's essay "Mysteries We Reread…" reprinted in Detecting Texts: The Metaphysical Detective Story from Poe to Postmodernism .

Related material—

Mathematics vulgarizer Robert Osserman died on St. Andrew's Day, 2011.

A Rhetorical Question

Osserman in 2004

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer


Above: Amy Adams in "Sunshine Cleaning"

Thursday, November 8, 2012


Filed under: General — Tags: — m759 @ 9:48 AM

Dante, Purgatorio XVI

Esce di mano a Lui, che la vagheggia
     Prima che sia, a guisa di fanciulla,
     Che piangendo e ridendo pargoleggia,

L’anima semplicetta, che sa nulla,
     Salvo che, mossa da lieto fattore,
     Volontier torna a ciò che la trastulla.

Dante on the soul in Purgatorio 16
Related material:

and, in this journal,

Sunday, July 22, 2012


Filed under: General — m759 @ 10:01 AM

"One ring to bring them all…"
— J. R. R. Tolkien, Catholic author

Today in History, July 22, by The Associated Press—

"In 1934, bank robber John Dillinger was shot to death
by federal agents outside Chicago's Biograph Theater,
where he had just seen the Clark Gable movie
'Manhattan Melodrama.'"

From a  Manhattan Melodrama

"Follow the Ring" 

Piatigorsky died on Sunday, July 15. Notes in this  journal from that date—


Tuesday, July 10, 2012

Euclid vs. Galois

Filed under: General,Geometry — Tags: — m759 @ 11:01 AM


Euclidean square and triangle

Galois square and triangle


This journal on the date of Hilton Kramer's death,
The Galois Tesseract, and The Purloined Diamond.

Wednesday, March 28, 2012


Filed under: General — m759 @ 9:29 AM

… of background for yesterday's Log24 posts

Aldaily.com, March 28 and 27, 2012

"Now that philosophy has become a scientific pursuit…."
 leads to the following article from St. Patrick's Day—

See also this  journal on St. Patrick's Day—

Doodle Dandy and The Purloined Diamond (scroll down).

Sunday, March 18, 2012

Square-Triangle Diamond

Filed under: General,Geometry — Tags: — m759 @ 5:01 AM

The diamond shape of yesterday's noon post
is not wholly without mathematical interest …

The square-triangle theorem

"Every triangle is an n -replica" is true
if and only if n  is a square.

IMAGE- Square-to-diamond (rhombus) shear in proof of square-triangle theorem

The 16 subdiamonds of the above figure clearly
may be mapped by an affine transformation
to 16 subsquares of a square array.

(See the diamond lattice  in Weyl's Symmetry .)

Similarly for any square n , not just 16.

There is a group of 322,560 natural transformations
that permute the centers  of the 16 subsquares
in a 16-part square array. The same group may be
viewed as permuting the centers  of the 16 subtriangles
in a 16-part triangular array.

(Updated March 29, 2012, to correct wording and add Weyl link.)

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