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.)

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

Doodle Dandy (continued)

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


See also Kells in this journal.

Friday, March 16, 2012

For the Clueless

Filed under: General — Tags: — m759 @ 7:11 AM

"And she provided him besides with a ball of thread,
bidding him to fasten the end of it to the entrance
of the Labyrinth, and unwind it as he went in, that
it might serve him as a clue to find his way out again."

— "Theseus and Ariadne," by Charles Morris

From "Ariadne's Clue," a post of March 1 last year—


The Watson here is not Emma, but Victor—


Thursday, March 15, 2012

The Head of Caesar

Filed under: General — Tags: — m759 @ 10:00 PM

Remarks on Citizen Kane  from The New York Times

"… a kind of metaphysical detective story…. At the end we realize that the fragments are not governed by any secret unity: the detested Charles Foster Kane is a simulacrum, a chaos of appearances.” Borges concluded by quoting Chesterton, "there is nothing more frightening than a labyrinth that has no center." *

* The actual quote is from a Father Brown mystery, "The Head of Caesar," "'What we all dread most,' said the priest in a low voice, 'is a maze with no centre….'"

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