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) —
“He pointed at the football
on his desk. ‘There it is.’”
– Glory Road
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
"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"
Dante, Purgatorio XVI
Esce di mano a Lui, che la vagheggia
Prima che sia, a guisa di fanciulla,
Che piangendo e ridendo pargoleggia, 87
L’anima semplicetta, che sa nulla,
Salvo che, mossa da lieto fattore,
Volontier torna a ciò che la trastulla. 90
Related material:
and, in this journal,
"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—
Backstory—
Euclidean square and triangle—
Galois square and triangle—
Background—
This journal on the date of Hilton Kramer's death,
The Galois Tesseract, and The Purloined Diamond.
… of background for yesterday's Log24 posts—
"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).
The diamond shape of yesterday's noon post
is not wholly without mathematical interest …
"Every triangle is an n -replica" is true
if and only if n is a square.
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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