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Monday, November 25, 2013

Figurate Numbers

Filed under: General,Geometry — Tags: — m759 @ 8:28 am

The title refers to a post from July 2012:

IMAGE- Squares, triangles, and figurate numbers

The above post, a new description of a class of figurate
numbers that has been studied at least since Pythagoras,
shows that the "triangular numbers" of tradition are not
the only  triangular numbers.

"Thus the theory of description matters most. 
It is the theory of the word for those 
For whom the word is the making of the world…." 

— Wallace Stevens, "Description Without Place"

See also Finite Relativity (St. Cecilia's Day, 2012).

Tuesday, September 19, 2023

Figurate Geometry

Filed under: General — Tags: — m759 @ 9:18 am

The above title for a new approach to finite geometry
was suggested by the old phrase "figurate numbers."

See other posts in this journal now tagged Figurate Geometry.

Update of 10 AM ET on Sept. 19, 2023 —

Related material from social media:

Update of 10:30 AM ET Sept. 19 —

A related topic from figurate geometry:

The square-to-triangle mapping problem.

Monday, September 18, 2023

The Passage of Time

Filed under: General — Tags: , — m759 @ 9:55 am

The figure above summarizes a new way of looking at 
so-called "figurate numbers." The old  way goes back
at least to the time of Pythagoras.

A more explicit presentation —

Saturday, January 4, 2020

Welcome to the Uncanny Valley Country Club

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

The previous post  suggests a look at some Robot Apocalypse  remarks:

Related material —

This  journal on the above Stranger Dimensions date —

"Thus the theory of description matters most. 
It is the theory of the word for those 

For whom the word is the making of the world…." 

— Wallace Stevens, "Description Without Place, VII"

See also Finite Relativity (St. Cecilia's Day, 2012).

Some other lines from "Description Without Place" —

"An age is green or red. An age believes

Or it denies. An age is solitude
Or a barricade against the singular man

By the incalculably plural."

Friday, November 29, 2013

Centered

Filed under: General — m759 @ 1:00 pm

"I have now come to the most difficult part of my story."

— George MacDonald

"265" — Page number and centered square number

"153" — Triangular number (as noted by St. Augustine)

"265/153" — Object Lesson

An accurate description of such number lore:

"These are odd facts, very suitable for puzzle columns
and likely to amuse amateurs, but there is nothing
in them which appeals much to a mathematician.
The proofs are neither difficult nor interesting—
merely a little tiresome. The theorems are not serious;
and it is plain that one reason (though perhaps not the
most important) is the extreme speciality of both the
enunciations and the proofs, which are not capable of
any significant generalization." — G. H. Hardy

See also some remarks on figurate numbers in this journal.

Nothing went wrong at the back of the north wind. 
Neither was anything quite right, he thought. 
Only everything was going to be right some day….

"What a queer place it must be!"

"It's a very good place."

"Do you want to go back again?"

"No; I don't think I have left it; I feel it here, somewhere."

"Did the people there look pleased?"

"Yes— quite pleased, only a little sad."

"Then they didn't look glad?"

"They looked as if they were waiting to be gladder some day."

— George MacDonald

Monday, November 25, 2013

Pythagoras Wannabe*

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

A scholium on the link to Pythagoras
in this morning's previous post Figurate Numbers:

For related number mysticism, see Chapter 8, "Magic Numbers,"
in Love and Math: The Heart of Hidden Reality, 
by Edward Frenkel (Basic Books, Oct. 1, 2013).

(Click for clearer image.)

See also Frenkel's Metaphors in this journal. 

* The wannabe of the title is of course not Langlands, but Frenkel.

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