Log24

Sunday, October 5, 2025

Overlapping

Filed under: General — m759 @ 9:32 am

A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because 
they are made with ideas.

G. H. Hardy, A Mathematician's Apology  (1940).

This post notes three uses of overlapping figures  in mathematics.

The idea  in each case is that of overlapping.

An old use of overlapping — probably well-known in ancient Greece:

Pythagorean theorem proof by overlapping similar figures

A more recent use of overlapping — Venn diagrams:

Venn diagram of three sets

My own personal use of overlapping —
half-circle patterns that led to the diamond theorem:

Thursday, September 18, 2025

“In other art news . . .”

Filed under: General — Tags: , — m759 @ 5:40 pm

Art from 1976 —

Art from 2025 —

A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because 
they are made with ideas.

G. H. Hardy, A Mathematician's Apology  (1940).

In other art news . . .

Saturday, September 6, 2025

Shaped Ideas

Filed under: General — Tags: , — m759 @ 11:39 am

A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because 
they are made with ideas.

G. H. Hardy, A Mathematician's Apology  (1940).
 

Overlapping Ideas 

Pythagorean theorem proof by overlapping similar figures

5:39 PM  Saturday, September 6, 2025 (GMT+2)
Time in Venice, Metropolitan City of Venice, Italy

Saturday, April 5, 2003

Saturday April 5, 2003

Filed under: General,Geometry — Tags: , — m759 @ 9:49 am

Art Wars:
Mathematics and the
Emperor's New Art

From Maureen Dowd's New York Times column of June 9, 2002: 

"The shape of the government is not as important as the policy of the government. If he makes the policy aggressive and pre-emptive, the president can conduct the war on terror from the National Gallery of Art."

 

NY Times, April 5, 2003:
U.S. Tanks Move Into Center of Baghdad
See also today's op-ed piece
by Patton's grandson.

Meanwhile, at the Washington Post, another example of great determination and strength of character:

 

Donald Coxeter Dies: Leader in Geometry

By Martin Weil
Washington Post Staff Writer
Saturday, April 5, 2003

"Donald Coxeter, 96, a mathematician who was one of the 20th century's foremost specialists in geometry and a man of great determination and strength of character as well, died March 31 at his home in Toronto."

From another Coxeter obituary:

In the Second World War, Coxeter was asked by the American government to work in Washington as a code-breaker. He accepted, but then backed out, partly because of his pacifist views and partly for aesthetic reasons: "The work didn't really appeal to me," he explained; "it was a different sort of mathematics."

For a differing account of how geometry is related to code-breaking, see the "Singer 7-cycle" link in yesterday's entry, "The Eight," of 3:33 PM.  This leads to a site titled

An Introduction to the
Applications of Geometry in Cryptography
.

"Now I have precisely the right instrument, at precisely the right moment of history, in exactly the right place."

 — "Patton,"
the film

Quod erat
demonstrandum
.


 

Added Sunday, April 6, 2003, 3:17 PM:

The New York Times Magazine of April 6
continues this Art Wars theme.


                 (Cover typography revised)

The military nature of our Art Wars theme appears in the Times's choice of words for its cover headline: "The Greatest Generation." (This headline appears in the paper, but not the Internet, version.)

Some remarks in today's Times Magazine article seem especially relevant to my journal entry for Michelangelo's birthday, March 6.

"…Conceptualism — suddenly art could be nothing more than an idea….

LeWitt moved between his syntax of geometric sculptures and mental propositions for images: concepts he wrote on paper that could be realized by him or someone else or not at all.  Physical things are perishable.  Ideas need not be."

— Michael Kimmelman, chief art critic of the New York Times, April 6, 2003

Compare this with a mathematician's aesthetics:

"A mathematician, like a painter or a poet, is a maker of patterns.  If his patterns are more permanent than theirs, it is because they are made with ideas."

— G. H. Hardy, A Mathematician's Apology (1940), reprinted 1969, Cambridge U. Press, p. 84 

It seems clear from these two quotations that the real conceptual art is mathematics and that Kimmelman is peddling the emperor's new clothes.

Powered by WordPress