Log24

Monday, January 8, 2018

Raiders of the Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 11:15 PM
 

The Quantum Tesseract Theorem 

 


 

Raiders —

A Wrinkle in Time
starring Storm Reid,
Reese Witherspoon,
Oprah Winfrey &
Mindy Kaling

 

Time Magazine  December 25, 2017 – January 1, 2018

Monday, May 9, 2016

Search for the Lost Theorem

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

The three Solomons of the previous post (LeWitt,
Marcus, and Golomb) suggest the three figures
-1, 0, and 1  symbols for the three elements
of the Galois field GF(3).  This in turn suggests a
Search for The Lost Theorem. Some cross-cultural
context:  The First of May, 2010.

Monday, October 13, 2014

Sallows on “The Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 9:30 PM

Parallelograms and the structure of the 3×3 array —

Click to enlarge:

A different approach to parallelograms and arrays —

Click for original post:

Raiders of the Lost Theorem

Filed under: General,Geometry — Tags: — m759 @ 12:05 PM

(Continued from Nov. 16, 2013.)

The 48 actions of GL(2,3) on a 3×3 array include the 8-element
quaternion group as a subgroup. This was illustrated in a Log24 post,
Hamilton’s Whirligig, of Jan. 5, 2006, and in a webpage whose
earliest version in the Internet Archive is from June 14, 2006.

One of these quaternion actions is pictured, without any reference
to quaternions, in a 2013 book by a Netherlands author whose
background in pure mathematics is apparently minimal:

In context (click to enlarge):

Update of later the same day —

Lee Sallows, Sept. 2011 foreword to Geometric Magic Squares —

“I first hit on the idea of a geometric magic square* in October 2001,**
and I sensed at once that I had penetrated some previously hidden portal
and was now standing on the threshold of a great adventure. It was going
to be like exploring Aladdin’s Cave. That there were treasures in the cave,
I was convinced, but how they were to be found was far from clear. The
concept of a geometric magic square is so simple that a child will grasp it
in a single glance. Ask a mathematician to create an actual specimen and
you may have a long wait before getting a response; such are the formidable
difficulties confronting the would-be constructor.”

* Defined by Sallows later in the book:

“Geometric  or, less formally, geomagic  is the term I use for
a magic square in which higher dimensional geometrical shapes
(or tiles  or pieces ) may appear in the cells instead of numbers.”

** See some geometric  matrices by Cullinane in a March 2001 webpage.

Earlier actual specimens — see Diamond Theory  excerpts published in
February 1977 and a brief description of the original 1976 monograph:

“51 pp. on the symmetries & algebra of
matrices with geometric-figure entries.”

— Steven H. Cullinane, 1977 ad in
Notices of the American Mathematical Society

The recreational topic of “magic” squares is of little relevance
to my own interests— group actions on such matrices and the
matrices’ role as models of finite geometries.

Saturday, November 16, 2013

Raiders of the Lost Theorem

Filed under: General,Geometry — Tags: , — m759 @ 11:30 AM

IMAGE- The 'atomic square' in Lee Sallows's article 'The Lost Theorem'

Yes. See

The 48 actions of GL(2,3) on a 3×3 coordinate-array A,
when matrices of that group right-multiply the elements of A,
with A =

(1,1) (1,0) (1,2)
(0,1) (0,0) (0,2)
(2,1) (2,0) (2,2)

Actions of GL(2,p) on a pxp coordinate-array have the
same sorts of symmetries, where p is any odd prime.

Note that A, regarded in the Sallows manner as a magic square,
has the constant sum (0,0) in rows, columns, both diagonals, and  
all four broken diagonals (with arithmetic modulo 3).

For a more sophisticated approach to the structure of the
ninefold square, see Coxeter + Aleph.

Sunday, June 12, 2016

Table Talk

Filed under: General,Geometry — m759 @ 1:00 PM

See also the previous post and posts on "The Lost Theorem."

Sunday, November 9, 2014

Twaddle

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM

“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”

— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121

Cf. Raiders of the Lost Theorem, Oct. 13, 2014.

See also tonight’s previous post and
“Feng Shui” in this journal.

Friday, October 17, 2014

Mathematics and Narrative, continued:

Filed under: General — Tags: — m759 @ 2:01 PM

Raiders of the Lost Archetype

“… an unexpected development: the discovery of a lost archetype….”

— “The Lost Theorem,” by Lee Sallows, Mathematical Intelligencer, Fall 1997

Related material:

A scene from the 1954 film:

A check of this  journal on the above MetaFilter date — Jan. 24, 2012 —
yields a post tagged “in1954.”  From another post with that tag:

Medal of 9/15/06

Backstory:  Posts tagged Root Circle.

Wednesday, October 15, 2014

Diabolically Complex

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

The title is from a Log24 post, "Diabolically Complex Riddle," of Sept. 27, 2014.

(See also a search for "Diabolic"  in this journal, which yields an application to
"magic" squares.)

From 'The Lost Theorem,' by Lee Sallows

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