Log24

"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

An inscription from 2010 —

An inscription from 1984 —

* See also other Log24 posts mentioning this phrase.

From St. Patrick's Day this year —

The March 17 post's title is a reference to a recent film.

The title refers to that of today's previous post, which linked to
a song from the June 1, 1983, album Synchronicity .
(Cf.  that term in this journal.)

For some work of my own from the following year, 1984, see…

… as well as the Orwellian dictum Triangles Are Square.

(The cubical figure at left above is from the same month,
if not the same day, as Synchronicity —  June 21, 1983.)

Update of May 27, 2013:
The post below is now outdated. See
http://planetmath.org/cullinanediamondtheorem .

__________________________________________________________________

The brief note on the diamond theorem at PlanetMath
disappeared some time ago. Here is a link to its
current URL: http://planetmath.org/?op=getobj;from=lec;id=49.

Update of 3 PM ET Jan. 2, 2013—

Another item recovered from Internet storage:

Click on the Monthly  page for some background.

For example—

A letter to the editor of the American Mathematical Monthly
from the June-July 1985 issue has—

For definitions, see the 1985 letter in Triangles Are Square.

(The 1984 lemma discussed there has now, in response to an article
in Wolfram MathWorld, been renamed the square-triangle theorem .)

A search today for related material yielded the following—

This was supplied, without attribution, as part of the official solution
to Problem 3 in the 17th Asian Pacific Mathematics Olympiad
from March 2005. Apparently it seemed obvious to the composer
of the problem. As the 1985 letter notes, it may be not quite  obvious.

At any rate, it served in Problem 3 as a lemma , in the sense
described above by Wikipedia. See related remarks by Doron Zeilberger.

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 .

MathWorld.Wolfram.com has an article titled "Square-Triangle Theorem."

An article of my own, whose HTML title was previously "Triangles are Square," has been retitled accordingly.