Log24

Saturday, April 30, 2022

The Artifact Mathematician

Filed under: General — Tags: , — m759 @ 2:25 pm

(For Harlan Kane)

See as well the Pearl Jam song in posts tagged Enigma Keys.

Deepening

Filed under: General — Tags: , — m759 @ 1:46 pm

(Expanding the Spielraum continues.)

Widening

Filed under: General — Tags: , — m759 @ 12:33 pm

"Damning revelations" — Marie Claire  yesterday

"Imagine a powerful man as a ship, like the Titanic. That ship is a huge enterprise. When it strikes an iceberg, there are a lot of people on board desperate to patch up holes — not because they believe in or even care about the ship, but because their own fates depend on the enterprise."

Op-ed attributed to Amber Heard by The Washington Post ,
December 18, 2018

Heart Heard

Filed under: General — m759 @ 11:40 am

"Nor mouth had, no nor mind, expressed
What heart heard of, ghost guessed:"

— Two lines from a Gerard Manley Hopkins poem
as quoted by Caleb Murdock at . . .

https://www.ablemuse.com/erato/showthread.php?t=5356 .

From that same URL —

"And, Caleb, yes, 'sprung rhythm' has made it into dictionaries,
though even there, the association is with Hopkins."

For guess-ghosts —

"Spring is sprung, the grass is riz,
I wonder where the flowers is."

And for an able muse —

Friday, April 29, 2022

The Diamond Theorem in Basque Country

Filed under: General — Tags: , — m759 @ 5:57 pm

Translated by Google as . . .

The Truchet Tiles and the Diamond Puzzle and
     The Art of the Simple Truchet Tile.

About the author: 

Raúl Ibáñez is a professor in the Department of Mathematics
at the UPV/EHU and collaborator with the Chair of Scientific Culture.

About his school:

The University of the Basque Country 
(Basque: Euskal Herriko UnibertsitateaEHU 
Spanish: Universidad del País VascoUPV UPV/EHU)
is a Spanish public university of the Basque Autonomous Community.
Wikipedia

“Welcome to the Garden Club …”

Filed under: General — m759 @ 5:11 pm

Continues.

Springtime for Wagner

Filed under: General — Tags: — m759 @ 4:48 pm

Metamorphosis:  Seed to Flower in New Yorker Propaganda

Filed under: General — Tags: , — m759 @ 3:21 pm

Illustration by Nicholas Konrad / The New Yorker   April 28, 2022

 

Some related material from Harvard — 
 

The Seed 

 

Code Bleu

Filed under: General — Tags: , , , — m759 @ 2:17 pm

From The New York Times  on May 5, 2011 —

"… What Paris says to me is love story, awash with painters,
shots of the Seine, Champagne. Thank God I have a
can’t-miss notion to sell you. I call it ‘Midnight in Paris.’ ”

“Romantic title,” I had to admit. “Is there a script?”

“Actually, there’s nothing on paper yet, but I can spitball
the main points,” he said, slipping on his tap shoes.

“Maybe some other time,” I said, mindful of Cubbage’s
unbroken string of theatrical Hiroshimas.

— Woody Allen

The above passage is in memory of a French film director
who, like the reporter in yesterday's post Primary Colors,
reportedly died on April 21, 2022.

See also Aitchison at Hiroshima and Easter for Aitchison.

Thursday, April 28, 2022

Primary Colors

Filed under: General — Tags: , , , — m759 @ 5:05 pm

The Usual Narratives … Dog Bites Man, Shit Hits Fan.

Filed under: General — Tags: — m759 @ 4:04 pm

"It was a bright cold day in April . . ."

 

The Tummelplatz

Filed under: General — m759 @ 8:47 am

"Leslie Jamison has written an honest and important book….
All in all, vivid writing and required reading." ―Stephen King

Meanwhile, also on April 5, 2018… See posts tagged D8.

More recently, in a conspicuously un-dated new literary magazine …

See as well Freud on the Tummelplatz .

Wednesday, April 27, 2022

Dealing with Cubism …

Filed under: General — Tags: , — m759 @ 3:01 pm

Continues.

See as well  today's previous post.

Ennead  (Pace Moon Knight)

Filed under: General — Tags: , , — m759 @ 1:33 pm

Putting the graphic  in lexicographic

'The 3x3 Magic Square as an Affine Transformation'

The Day of the Principles

Filed under: General — Tags: — m759 @ 5:24 am

Tuesday, April 26, 2022

Sermon

Filed under: General — m759 @ 1:09 pm

From a post titled "Sermon," August 20, 2017 —

 

 

The Nocciolo

Filed under: General — Tags: , , — m759 @ 10:47 am

For a Kaleidoscopic Structuralist

Adapted from a Log24 post of October  25, 2006.

Monday, April 25, 2022

Annals of Mathematical History

Filed under: General — Tags: , — m759 @ 11:42 pm

Bourbaki on arithmetic and geometry

Some related remarks —

IMAGE- History of Mathematics in a Nutshell

From the Finland Station

Filed under: General — Tags: , — m759 @ 2:38 pm

Vienna Fantasies

Filed under: General — Tags: — m759 @ 12:04 pm

From a post of November 7, 2012 —

I Ching chessboard (original 1989 arrangement)

Meanwhile, in fiction —

Another Vienna fantasy —

Vide  the source.

Sunday, April 24, 2022

The Well and the Stone

Filed under: General — Tags: , — m759 @ 10:29 pm

From a post of October 25, 2002 —

"A work of art has an author and yet,
when it is perfect, it has something
which is essentially anonymous about it."
— Simone Weil, Gravity and Grace

This flashback was suggested by a quotation
in today's previous post

"Go back to the darkest roots of civilisation
and you will find them knotted round
some sacred stone or encircling
some sacred well."

— G. K. Chesterton, Orthodoxy , Ch. 5 
"The Flag of the World."

Roots

Filed under: General — Tags: — m759 @ 2:32 pm

"Go back to the darkest roots of civilisation
and you will find them knotted round
some sacred stone or encircling
some sacred well."

— G. K. Chesterton, Orthodoxy , Ch. 5
"The Flag of the World."

See also . . .

Structuralism: Three Betweens

Filed under: General — Tags: , , , — m759 @ 10:44 am
 

Tuesday, November 3, 2009

Summa Mythologica

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

Book review by Jadran Mimica in Oceania, Vol. 74, 2003:

"In his classic essay of 1955 'The Structural Study of Myth' Levi-Strauss came up with a universal formula of mythopoeic dynamics

[fx(a) : fy(b) :: fx(b) : fa-1(y)]

that he called canonical 'for it can represent any mythic transformation'. This formulation received its consummation in the four massive Mythologiques volumes, the last of which crystallises the fundamental dialectics of mythopoeic thought: that there is 'one myth only' and the primal ground of this 'one' is 'nothing'. The elucidation of the generative matrix of the myth-work is thus completed as is the self-totalisation of both the thinker and his object."

So there.

At least one mathematician has claimed that the Levi-Strauss formula makes sense. (Jack Morava, arXiv pdf, 2003.)

I prefer the earlier (1943) remarks of Hermann Hesse on transformations of myth:

"…in the spirit of the Glass Bead Game, everything actually was all-meaningful, that every symbol and combination of symbols led not hither and yon, not to single examples, experiments, and proofs, but into the center, the mystery and innermost heart of the world, into primal knowledge. Every transition from major to minor in a sonata, every transformation of a myth or a religious cult, every classical or artistic formulation was, I realized in that flashing moment, if seen with a truly meditative mind, nothing but a direct route into the interior of the cosmic mystery, where in the alternation between inhaling and exhaling, between heaven and earth, between Yin and Yang, holiness is forever being created."

Saturday, April 23, 2022

Kaleidoscopic Structuralism

Filed under: General — Tags: , , — m759 @ 2:10 pm

The previous post suggests two quotes by Elizabeth Janeway 
from her review of the second volume of The Human Predicament ,
an unfinished trilogy by Richard Hughes.

"The Human Predicament  poses a universal question, and Hughes
is grappling with it really as a structuralist  philosopher."

"Hughes's style is kaleidoscopic , the shaking of vivid moments together
until a pattern emerges." 

— The New York Times Book Review Sunday, August 19, 1973, page 2

For a less literary example of kaleidoscopic structuralism, see
a Log24 post from the first anniversary of Janeway's reported death.

Related vocabulary —

Plato, Shakespeare, Et Cetera

Filed under: General — Tags: , , — m759 @ 1:27 pm

    See as well "Plato and Shakespeare" in this  journal.

Friday, April 22, 2022

“The History of the Concept of Structure”

Filed under: General — Tags: , — m759 @ 2:41 pm
 

Derrida was the final speaker on the final day. He remained a silent observer for much of the symposium. He looked on as Lacan rose to his feet with obscure questions at the end of each lecture, and as Barthes gently asked for clarification on various moot points. Eventually, however, Derrida, unused to speaking to large audiences, took to the stage, quietly shuffled his notes, and began, ‘Perhaps something has occurred in the history of the concept of structure that could be called an “event”…’ He spoke for less than half an hour. But by the time he was finished the entire structuralist project was in doubt, if not dead. An event had occurred: the birth of deconstruction.

Salmon, Peter. An Event, Perhaps  (pp. 2-3).
Verso Books (Oct. 2020). Kindle Edition. 

Salmon today at Arts & Letters Daily

Pleasantly Discursive Day* in the East

Filed under: General — Tags: — m759 @ 11:32 am

* Vide  "pleasantly discursive" in this journal.

Dies Natalis

Filed under: General — m759 @ 10:39 am

October 2, 2016, was, in the Catholic sense, the dies natalis
of a philosopher of science, Mary Hesse.

October 2 was also the day of birth, in the non-Catholic sense,
of philosopher-poet Wallace Stevens.

Cf.  remarks in this  journal on October 2, 2016.

Thursday, April 21, 2022

Change Arises  Continues

Filed under: General — Tags: — m759 @ 3:26 pm

(See Change Arises in this journal.)

See as well Log24 posts now tagged Dec. 16-18, 2013.

Mad Men and Broadway

Filed under: General — m759 @ 8:31 am

See as well Morse in Log24 posts on the Go chip.

For Arfken

Filed under: General — Tags: , , — m759 @ 7:34 am

Wednesday, April 20, 2022

Physics for Poets

Filed under: General — Tags: , , — m759 @ 9:23 am

Excerpt from a long poem by Eliza Griswold


The square array above does not  contain Arfken's variant
labels
for ρ1, ρ2, and ρ3, although those variant labels were
included in Arfken's 1985 square array and in Arfken's 1985
list of six anticommuting sets, copied at MathWorld as above.
The omission of variant labels prevents a revised list of the
six anticommuting sets from containing more  distinct symbols
than there are matrices.

Revised list of anticommuting sets:

α1   α2   α3  ρ2  ρ3

γ1   γ2   γ3   ρ1   ρ

δ δ2   δ ρ1   ρ2 

α1    γ1   δσ2  σ3 

α  γ2   δσ1   σ3

α  γ3   δ3  σ1   σ2  .

Context for the poem: Quark Rock.
Context for the physics: Dirac Matrices.

Tuesday, April 19, 2022

Hat Tip to Andrew Cusack

Filed under: General — Tags: , — m759 @ 9:03 pm

For a weblog post today on an auction item from
the collection of the late Pierre Le-Tan.

A search for information on Le-Tan reveals that his
dies natalis (in the Catholic sense) was Sept. 17, 2019.

See a poem quoted here on that date in posts tagged Quark Rock.

Reading Marks

Filed under: General — Tags: , — m759 @ 12:44 pm

 

 

( Not to be confused with The Tin Man’s Hat. )

Monday, April 18, 2022

Under the April Snow

Filed under: General — m759 @ 10:55 pm

"Spirits rise . . . ." — Streisand

Related material —

A 1920 play by J. M. Barrie, recreated on stage and now in film.

Developing

Filed under: General — Tags: — m759 @ 2:02 pm

For the Church of Perfect Coordinates*

Filed under: General — Tags: — m759 @ 1:22 pm

https://blacklistdeclassified.net/2022/04/15/
%f0%9f%94%b4-script-916-helen-maghi/
 —

Red: If I may offer some counsel –
Do not go where the path may lead.
Go instead where there is no path
and leave a trail.” 
In the spirit of that, I bring an unusual case….

This post is in honor of Thandiwe Newton,
who left a Westworld trail —

Vide  Bulk Apperception.

* Cf.  a post from Day 3 of 2022.

A Space Between

Filed under: General — Tags: , , — m759 @ 12:14 pm

From yesterday's post "Annals of Iconic Simplicity" —

On the founding of Princeton Architectural Press:

"'There was a space between the academic,
theory-heavy M.I.T. Press and the coffeetableism
of Rizzoli,' Mr. Lamster wrote, adding that
Princeton Architectural Press would fill the gap
with 'the voice of the young practitioner.'"

Some context —

Iconic Simplicity

Filed under: General — Tags: , — m759 @ 11:38 am

An illustration from posts tagged Holy Field GF(3) —

IMAGE- Elementary Galois Geometry over GF(3)

See also a Log24 search for "Four Gods."

Sunday, April 17, 2022

Annals of Iconic Simplicity

Filed under: General — Tags: — m759 @ 4:16 pm

The New York Times today has an obituary for
Kevin Lippert, the founder and publisher of
Princeton Architectural Press, who reportedly
died at 63 on March 29, 2022.

“'There was a space between the academic,
theory-heavy M.I.T. Press and the coffeetableism
of Rizzoli,' Mr. Lamster wrote, adding that
Princeton Architectural Press would fill the gap
with 'the voice of the young practitioner.'

Mr. Lippert championed emerging architects.
He published Steven Holl’s seminal architectural
manifesto, 'Anchoring,' in 1989, and wrote the
introduction to the book of the same name.
Mr. Holl, in a tribute to Mr. Lippert on his website,
called him 'a committed intellectual and impresario
for the culture of architecture.'”

— Katharine Q. Seelye, April 17, 2022, 2:21 p.m. ET

From the cited tribute to Lippert on Holl's website —

"An excerpt from his publisher’s foreword to Anchoring 

In its iconic simplicity, his work seems to be about
the language of architecture, not in the allusive sense
used by postmodernists nor in the paradigmatic sense
used by so-called 'deconstructivists' but at the level of
essences of tropes and morphs He is the only
American architect of his generation to be directly
influenced by the main lines in modern philosophy and
music, that is to say, by the line leading from Husserl
through to Heidegger and by separate achievements
of Bartok and Schonberg .
"

Actually, although the above "iconic simplicity" passage,
up to the ellipsis after "morphs,"  is  from the foreword
by Lippert, the references that follow the ellipsis — to
Husserl, Heidegger, Bartok, and Schonberg — are not
from Lippert's foreword, but from the introduction  by
one Kenneth Frampton

From Google Books:

Bibliographic data —

Another architectural memorial, from the reported date of Lippert's death —

Easter for Aitchison*

Filed under: General — Tags: , — m759 @ 7:07 am

* See other posts tagged Aitchison in this journal.

Saturday, April 16, 2022

The Quantum Tummelplatz

Filed under: General — Tags: , — m759 @ 10:28 am

For the De las Cuevas above, see 

https://www.gemmadelascuevas.com/

"I am an Assistant Professor at the Institute for Theoretical Physics
at the University of Innsbruck (Austria) . . . ." 

— and a tweet from Thursday, April 14, 2022, that indicates 
an interest in philosophy as well as physics —

Related vocabulary —

Related drama —

Friday, April 15, 2022

The Big Interview

Filed under: General — Tags: — m759 @ 11:16 pm

Why is this interview different from all other interviews?

Location, Location, Location

Filed under: General — m759 @ 12:54 pm

Draft of a letter to FDR written by Leo Szilard
and signed by Albert Einstein —

For the letter as sent  , see a webpage on the Manhattan Project.

This post was suggested by a New York Times obituary today that
contained the following misleading description — 

"a 1939 letter from Albert Einstein to President Franklin D. Roosevelt
encouraging the American effort to build the atomic bomb."

There was apparently no such effort until after the letter was received.

Thursday, April 14, 2022

Ouellette vs. the Cube

Filed under: General — Tags: — m759 @ 9:05 am

From the 2019 post Spring Loaded

British cover (2011) for 'From Eternity to Here,' by Sean Carroll

A more recent image, from Carroll's wife Jennifer Ouellette —

For a more sophisticated approach to the 4x4x4 cube,
see a page at finitegeometry.org.

The Heisenberg Potion

Filed under: General — Tags: — m759 @ 7:44 am

From the previous post

Many will prefer snazzier potions —

These were  available as NFTs recently . . .

See some.place. And then there is nine.place.

Wednesday, April 13, 2022

Dealing with Cubism continues . . .

Filed under: General — Tags: , — m759 @ 9:44 am

From Blue Cube Group  (April 7, 2022) —

A Bouquet for Levy

Tuesday, April 12, 2022

Dealing with Cubism

Filed under: General — Tags: , — m759 @ 10:45 am

"It’s important, as art historian Reinhard Spieler has noted,
that after a brief, unproductive stay in Paris, circa 1907,
Kandinsky chose to paint in Munich. That’s where he formed
the Expressionist art group Der Blaue Reiter  (The Blue Rider) —
and where he avoided having to deal with cubism."

— David Carrier, 

Images from an earlier Christmas Day, in 2005 —

The Eightfold Cube

The image “http://www.log24.com/theory/images/EightfoldWayCover.jpg” cannot be displayed, because it contains errors.

Monday, April 11, 2022

Holy Week: A Midrash for Levy

Filed under: General — Tags: — m759 @ 11:00 am

"Jesus Christ, Adam. I need you to play it cool."

See as well this journal on February 10, 2010 —

A Midrash for Levy

Sunday, April 10, 2022

Plan 9 Continues . . .

Filed under: General — Tags: , , — m759 @ 10:26 pm

A meditation on Coxeter's Aleph

'The 3x3 Magic Square as an Affine Transformation'

Turning Nine continues.

Filed under: General — Tags: — m759 @ 1:31 pm

That was then, this is now —

Be careful what you wish for.

“Program or be programmed” — Douglas Rushkoff

Filed under: General — Tags: , , — m759 @ 6:49 am

For the Unicorn School —

<time class="_1o9PC" 
datetime="2022-04-10T06:41:25.000Z" 
title="Apr 10, 2022">4 hours ago
</time>

From posts tagged Unicorn Language

http://www.log24.com/log/pix10B/100915-UnicornCross.jpg

Some will prefer the Dragon School . . .

of Tom Hiddleston, Emma Watson, and Humphrey Carpenter.

"National Unicorn Day" was yesterday .  Today's mythical creature —
the villainous spymaster of The Eiger Sanction , Yurasis Dragon.

Munro Doctrines

Filed under: General — m759 @ 5:38 am

The previous post was in memory of one Eleanor  Munro.

A different literary Munro —

Nobel Prize winner Alice Munro on fiction and the structure of space

And then there is Hector Hugh  Munro, pen name Saki . . .

See lumber room  in this journal (Nov. 30 – Dec. 3, 2016), and
later Ghost Ship  tales in a post of December 22, 2016.

Saturday, April 9, 2022

Readings for Remembrance

Filed under: General — m759 @ 7:00 pm

The author of the above title is featured in
a New York Times  obituary today. Another 
book by the same author, On Glory Roads,
appears in some related readings here .

Academic Rhetoric

Filed under: General — m759 @ 8:52 am

Also on the above publication date —

A related noun

The Conrad coinage —

Conrad K. Die beginnende Schizophrenie. 
Stuttgart, Germany: Thieme Verlag; 1958. 

Conrad K. Gestaltanalyse und Daseinsanalytik. 
Nervenarzt. 1959; 30: 405–410. 

Friday, April 8, 2022

A Comment for Ibsen

Filed under: General — m759 @ 3:41 pm

"Reviewing Ms. Allen’s staging of Ibsen’s
'When We Dead Awaken'
at Stage West in 1977, Mr. Barnes wrote that
it had 'speed, conviction and perception.'"

— Richard Sandomir today reviewing the life of Rae Allen.

From the conclusion of that Ibsen play

"Pax vobiscum."

See as well the YouTube comments below, on Allen
in the film version (1958) of "Damn Yankees" —

The Ugly Lesson:   Time Is Money

Filed under: General — Tags: , — m759 @ 1:11 pm

The above out-of-context quotation illustrates the following lesson,
from the Amazon.com page quoted in this moning's Souls at Stanford  —

See as well 1949  in the April 7 post
            The Usual Suspects.

Triangle Song

Filed under: General — Tags: — m759 @ 7:32 am

"Accepting the award, Mr. Logan said, 'I have a hunch
that this is as near to immortality as I'll ever get.'" 

— Mel Gussow in The New York Times, March 10, 1975

Souls at Stanford

Filed under: General — Tags: — m759 @ 6:00 am

Thursday, April 7, 2022

The Usual Suspects

Filed under: General — Tags: , — m759 @ 11:22 am

In memory of a musical that opened on this date —
April 7 — in 1949 . . .

See the same date in The Source , by James Michener (1965):

Blue Cube Group

Filed under: General — Tags: , , , — m759 @ 10:47 am

For more advanced students . . .

.

Hillbilly Politics:   News of the World, Second Wave

Filed under: General — Tags: — m759 @ 3:46 am

News of the World . . . Personalized.

Filed under: General — Tags: , — m759 @ 2:22 am

Wednesday, April 6, 2022

Dia Space

Filed under: General — Tags: , , , — m759 @ 4:20 pm

The date of the above post
was also the date of . . .

Analytic Continuation —

For Rydell High

Filed under: General — Tags: — m759 @ 6:03 am

Programmes: Architectural Theory and the Separatrix

Filed under: General — Tags: , , , — m759 @ 3:19 am

Architectural theorist Jeffrey Kipnis in 1991, recalled here in 2015 —

For the source of the illustration, see Hexagram 14.

Programmes: Warburgian vs. Hessian

Filed under: General — Tags: — m759 @ 2:43 am

For the former, see Warburg in this journal.
For the latter, see beadgame.space on the Web.

Tuesday, April 5, 2022

“Analysis.” — Dr. Robert Ford in “Westworld”

Filed under: General — Tags: , , — m759 @ 2:23 pm

"Godard, in the final analysis, expands the Warburgian programme
of iconology into that of a cinematographic iconology of the interstice."

— The author of the essay quoted in the previous post.

For a Maker of Strings Who Died on March 30

Filed under: General — m759 @ 5:41 am

Related material: Blue Guitar.

Monday, April 4, 2022

Pythagoras via Tao, Polya, and Euclid

Filed under: General — Tags: , — m759 @ 2:52 pm

From a post of April 1

A related post by Terry Tao on September 14, 2007 —

The comments on Tao's post contain a reference to Polya's classic
Induction and Analogy in Mathematics . (See pp. 15-17.) Polya notes 
on page 15 —

"Generalization, Specialization, and Analogy often concur
in solving mathematical problems.  Let us take as an example
the proof of the best known theorem of elementary geometry,
the theorem of Pythagoras. The proof that we shall discuss is
not new; it is due to Euclid himself (Euclid VI, 31)."

History of Mathematics . . . As It Is Writ

Filed under: General — Tags: — m759 @ 5:02 am

Here We Go Round the Prickly Pear . . .

Filed under: General — m759 @ 4:02 am

Sunday, April 3, 2022

Non-Dreams

Filed under: General — Tags: — m759 @ 7:29 pm

Compare and contrast with the Glass-Bead  essay in the previous post

The Caramello essay is backed up by some impressive technical work:

Dreams

Filed under: General — Tags: — m759 @ 8:35 am

Some may prefer a different sort of dream . . .

Background for the Stimmung  dream, from May 2019 —

For a different type of lifeworld, see May 2019 in this  journal.

Six AM Sunday

Filed under: General — Tags: — m759 @ 6:00 am

Saturday, April 2, 2022

Special Talents

Filed under: General — Tags: — m759 @ 7:47 pm

See Mimzy.xyz and Mimsy.xyz.

Plan 9 Continues.

Filed under: General — m759 @ 5:46 am

Click to enlarge.

Friday, April 1, 2022

An Obit for the Movie-Teller*…

Filed under: General — m759 @ 9:52 pm

 From the online New York Times  this evening.

* Vide  that phrase in this  journal.
   See also the previous post and . . .

On Sept. 12, 2001, The Washington Post published 
an opinion essay by General Boyd in which he wrote,
“While we may feel at the moment as though we are
in a trance, we are, in fact, awakening.”

— Katharine Q. Seelye in the general's obituary.

Beauty Bare … ?

Filed under: General — Tags: , — m759 @ 12:00 am

Pythagorean theorem proof by similarly divided squares

Update of 11:30 AM ET April 1, 2022 — A simpler version:

The above picture may be used to to introduce the concept of a "shape constant"
in similar figures — like the shape constant pi  in a circle or the square root of 2
in a square. In each of the three similar figures at right above, the ratio of the
triangular area to the area of the attached square is a shape constant  
the same, because of their similarity, for each of the three shapes. Since the
areas of the top two triangles at right sum to that of the enclosed triangle at left,
their attached square areas sum to the area of the bottom square, Q.E.D.

The source of the proof —

Pythagorean-theorem proof using similar triangles and concept of 'shape constant' m

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