Sunday, July 19, 2020

Ornaments for Valéry*

Filed under: General — Tags: , — m759 @ 12:27 AM

* See Valéry Ornament in this journal.

Sunday, January 19, 2014

Deep Beauty

Filed under: General — Tags: , — m759 @ 11:00 AM


Old punchline:  “Spell chrysanthemum.”
Variation:  “Spell coordinatization.”

Related test:  Chrysanthemum Coordinatization —

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Context Root circle.

Saturday, January 18, 2014

The Triangle Relativity Problem

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

A sequel to last night’s post The 4×4 Relativity Problem —

IMAGE- Triangle Coordinatization

In other words, how should the triangle corresponding to
the above square be coordinatized ?

See also a post of July 8, 2012 — “Not Quite Obvious.”

Context — “Triangles Are Square,” a webpage stemming
from an American Mathematical Monthly  item published
in 1984.

Friday, January 17, 2014

The 4×4 Relativity Problem

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

The sixteen-dot square array in yesterday’s noon post suggests
the following remarks.

“This is the relativity problem:  to fix objectively a class of
equivalent coordinatizations and to ascertain the group of
transformations S mediating between them.”

— Hermann Weyl, The Classical Groups ,
Princeton University Press, 1946, p. 16

The Galois tesseract  appeared in an early form in the journal
Computer Graphics and Art , Vol. 2, No. 1, February 1977—

IMAGE- Hypercube and 4x4 matrix from the 1976 'Diamond Theory' preprint, as excerpted in 'Computer Graphics and Art'

The 1977 matrix Q is echoed in the following from 2002—

IMAGE- Dolgachev and Keum, coordinatization of the 4x4 array in 'Birational Automorphisms of Quartic Hessian Surfaces,' AMS Transactions, 2002

A different representation of Cullinane’s 1977 square model of the
16-point affine geometry over the two-element Galois field GF(2)
is supplied by Conway and Sloane in Sphere Packings, Lattices and Groups   
(first published in 1988) :

IMAGE- The Galois tesseract as a four-dimensional vector space, from a diagram by Conway and Sloane in 'Sphere Packings, Lattices, and Groups'

Here a, b, c, d   are basis vectors in the vector 4-space over GF(2).
(For a 1979 version of this vector space, see AMS Abstract 79T-A37.)

See also a 2011 publication of the Mathematical Association of America —

From 'Beautiful Mathematics,' by Martin Erickson, an excerpt on the Cullinane diamond theorem (with source not mentioned)

Thursday, January 16, 2014

Confession of a Sucker

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

Today’s 11 AM (ET) post was suggested by a New York Times
article, online yesterday, about art gallery owner Lisa Cooley.

A check of Cooley’s website yields the image below,
related to Beckett’s Molloy .

For the relevant passage from Molloy , click the following:

I took advantage of being at the seaside
to lay in a store of sucking-stones.

For posts on Molloy  in this journal, click Beckett + Molloy .

Cynthia Daignault, 2011:
The one I shall now describe, if I can…
Oil on linen, in 2 parts: 40 x 30 inches, 96 x 75 inches

Related art theory —

Geometry of the 4×4 Square 

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