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Monday, July 27, 2026

Note for a Jain Temple:
Magic Objects in Every Dimension

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

From ICM Invited Lectures & Panels for July 27, 2026:

Bhargava —

"Inscribed on a wall near the entrance of the majestic Parshvanath Jain Temple in Khajuraho, India (built around 960 CE) is a 4 × 4 magic square with remarkable arithmetic properties. We will explain why this magic square is the unique one of its kind, up to certain transformations.  This answers a question posed by the legendary geometer HSM Coxeter in 1938.  We will also explain why there is a unique such magic object in every dimension."

Related reading

Saturday, November 30, 2013

Waiting for Ogdoad

Filed under: General,Geometry — Tags: , , , — m759 @ 10:30 am

Continued from October 30 (Devil’s Night), 2013.

“In a sense, we would see that change
arises from the structure of the object.”

— Theoretical physicist quoted in a
Simons Foundation article of Sept. 17, 2013

This suggests a review of mathematics and the
“Classic of Change ,” the I Ching .

The physicist quoted above was discussing a rather
complicated object. His words apply to a much simpler
object, an embodiment of the eight trigrams underlying
the I Ching  as the corners of a cube.

The Eightfold Cube and its Inner Structure

See also…

(Click for clearer image.)

The Cullinane image above illustrates the seven points of
the Fano plane as seven of the eight I Ching  trigrams and as
seven natural ways of slicing the cube.

For a different approach to the mathematics of cube slices,
related to Gauss’s composition law for binary quadratic forms,
see the Bhargava cube  in a post of April 9, 2012.

Monday, April 9, 2012

Eightfold Cube Revisited

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

A search today (Élie Cartan's birthday) for material related to triality*

Dynkin diagram D4 for triality

yielded references to something that has been called a Bhargava cube .

Two pages from a 2006 paper by Bhargava—

Bhargava's reference [4] above for "the story of the cube" is to…

Higher Composition Laws I:
A New View on Gauss Composition,
and Quadratic Generalizations

Manjul Bhargava

The Annals of Mathematics
Second Series, Vol. 159, No. 1 (Jan., 2004), pp. 217-250
Published by: Annals of Mathematics
Article Stable URL: http://www.jstor.org/stable/3597249

A brief account in the context of embedding problems (click to enlarge)—

For more ways of slicing a cube,
see The Eightfold Cube —

* Note (1) some remarks by Tony Smith
   related to the above Dynkin diagram
   and (2) another colorful variation on the diagram.

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