Log24

Sunday, June 10, 2018

Pieces of April

Filed under: General — Tags: — m759 @ 12:25 AM

This journal on April 16, 2018 —

Happy birthday to Pope Emeritus Benedict XVI.

Related material from another weblog in a post also dated April 16, 2018 —

"As I write this, it’s April 5, midway through the eight-day
festival of Passover. During this holiday, we Jews air our
grievances against the ancient Pharaoh who enslaved
and oppressed us, and celebrate the feats of strength
with which the Almighty delivered us from bondage —
wait a minute, I think I’m mixing up Passover with Festivus."
. . . .

"Next month: Time and Tesseracts."

From that next post, dated May 16, 2018 —

"The tesseract entered popular culture through
Madeleine L’Engle’s 'A Wrinkle in Time' . . . ."

The post's author, James Propp, notes that

" L’Engle caused some of her readers confusion
when one of the characters … the prodigy
Charles Wallace Murray [sic ] , declared 'Well, the fifth
dimension’s a tesseract.' "

Propp is not unfamiliar with prodigies:

"When I was a kid living in the Long Island suburbs,
I sometimes got called a math genius. I didn’t think
the label was apt, but I didn’t mind it; being put in
the genius box came with some pretty good perks."

— "The Genius Box," a post dated March 16, 2018

To me, Propp seems less like Charles Wallace
and more like the Prime Coordinator —

For further details, see the following synchronicity checks:

Propp March 16     Log24 March 16

Propp April 16        Log24 April 16

Propp May 16        Log24 May 16 .

Tuesday, April 17, 2018

A Necessary Possibility*

Filed under: General,Geometry — m759 @ 10:00 AM

"Without the possibility that an origin can be lost, forgotten, or
alienated into what springs forth from it, an origin could not be
an origin. The possibility of inscription is thus a necessary possibility,
one that must always be possible."

— Rodolphe Gasché, The Tain of the Mirror ,
     Harvard University Press, 1986

IMAGE- Harvard University Press, 1986 - A page on Derrida's 'inscription'

An inscription from 2010 —

An inscription from 1984 —

American Mathematical Monthly, June-July 1984, p. 382

MISCELLANEA, 129

Triangles are square

"Every triangle consists of  n congruent copies of itself"
is true if and only if  n is a square. (The proof is trivial.) 
— Steven H. Cullinane

* See also other Log24 posts mentioning this phrase.

Monday, April 16, 2018

The Brooklyn Game

Filed under: General — Tags: — m759 @ 2:12 PM

"Can you bring me some players?"

— Molly Bloom in "Molly's Game"

Happy birthday to Pope Emeritus Benedict XVI.

Sunday, April 15, 2018

Colorado Olympiad

Filed under: General,Geometry — Tags: — m759 @ 1:01 PM

Or:  Personalities Before Principles

Personalities —

Principles —

This  journal on April 28, 2004 at 7:00 AM.

Backstory —

Square Triangles in this journal.

Sunday, February 12, 2017

Religious Art for Sunday

Filed under: General,Geometry — m759 @ 11:02 AM

Euclidean  square and triangle

Galois  square and triangle

For some backstory, see the "preface" of the 
previous post and Soifer in this journal.

Thursday, January 14, 2016

“Henceforth S-S”

Filed under: General — m759 @ 3:07 PM

University of Colorado professor Alexander Soifer has written
a sharp reply to a review of his recent book on the noted
mathematician B. L. van der Waerden (1903-1996).

See in the February issue, online today, of the Notices of the
American Mathematical Society 
, Letters to the Editor.

Soifer's letter begins

"The critical September 2015 Notices  review of
my new book 'The Scholar and the State' by
Reinhard Siegmund-Schultze (henceforth S-S)
contradicted his decade of enthusiastic comments
on all my publications about Van der Waerden (VdW)."

Material from this  journal related to the initials "S-S"
and to today's previous post

Posts now tagged Soul Notes.

Sunday, August 16, 2015

Mathematics History

Filed under: General — m759 @ 6:25 PM

The following book is reviewed in the September 2015
Notices of the American Mathematical Society

The reviewer is Reinhard Siegmund-Schultze, a professor
at the University of Agder in Kristiansand (Norway). 

See also references to the book's author in this  journal.

Tuesday, July 10, 2012

Euclid vs. Galois

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

(Continued)

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.

Saturday, July 7, 2012

Quartet

Filed under: General,Geometry — m759 @ 1:23 PM

"Euclid (Ancient Greek: Εὐκλείδης Eukleidēs), fl. 300 BC, 
also known as Euclid of Alexandria, was a Greek
mathematician, often referred to as the 'Father of Geometry.'"

— Wikipedia

A Euclidean quartet (see today's previous post)—

IMAGE- Triangle cut into four congruent subtriangles
Image by Alexander Soifer

See also a link from June 28, 2012, to a University Diaries  post
discussing "a perfection of thought."

Perfect means, among other things, completed .

See, for instance, the life of another Alexandrian who reportedly
died on the above date—

"Gabriel Georges Nahas was born in Alexandria, Egypt, on
 March 4, 1920…."

 — This afternoon's online New York Times

Étude

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM

 IMAGE- Google Books ad for 'Geometric Etudes in Combinatorial Mathematics,' by Alexander Soifer

IMAGE- Triangle cut into four congruent subtriangles

For remarks related by logic, see the square-triangle theorem.

For remarks related by synchronicity, see Log24 on
the above publication date,  June 15, 2010.

According to Google (and Soifer's page xix), Soifer wants to captivate
young readers.

Whether young readers should  be captivated is open to question.

"There is  such a thing as a 4-set."

Update of 9:48 the same morning—

Amazon.com says Soifer's book was published not on June 15, but on
 June 29 , 2010
(St. Peter's Day).

Thursday, March 22, 2012

Square-Triangle Theorem continued

Filed under: General,Geometry — m759 @ 6:00 AM

Last night's post described a book by Alexander Soifer
on questions closely related to— and possibly
suggested by— a Miscellanea  item and a letter to
the editor
in the American Mathematical Monthly ,
June-July issues of 1984 and 1985.

Further search yields a series of three papers by
Michael Beeson on the same questions. These papers are
more mathematically  presentable than Soifer's book.

Triangle Tiling I 

http://www.michaelbeeson.com/research/papers/TriangleTiling1.pdf

       March 2, 2012

Triangle Tiling II 

http://www.michaelbeeson.com/research/papers/TriangleTiling2.pdf

       February 18, 2012

Triangle Tiling III 

http://www.michaelbeeson.com/research/papers/TriangleTiling3.pdf

       March 11, 2012 

These three recent preprints replace some 2010 drafts not now available.
Here are the abstracts of those drafts—

"Tiling triangle ABC with congruent triangles similar to ABC"
 (March 13, 2010),

"Tiling a triangle with congruent triangles"
(July 1, 2010).

Beeson, like Soifer, omits any reference to the "Triangles are square" item
of 1984 and the followup letter of 1985 in the Monthly .

Wednesday, March 21, 2012

Square-Triangle Theorem

Filed under: General,Geometry — m759 @ 10:30 PM

(Continued from March 18, 2012)

Found in a search this evening—

How Does One Cut a Triangle?  by Alexander Soifer

(Second edition, Springer, 2009. First edition published
by Soifer's Center for Excellence in Mathematical Education,
Colorado Springs, CO, in 1990.)

This book, of xxx + 174 pages, covers questions closely related
to the "square-triangle" result I published in a letter to the 
editor of the June-July 1985 American Mathematical Monthly
(Vol. 92, No. 6, p. 443).  See Square-Triangle Theorem.

Soifer's four pages of references include neither that letter
nor the Monthly  item, "Miscellaneum 129: Triangles are square"
of a year earlier that prompted the letter.

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