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Tuesday, December 7, 2021

Tortoise Variations

Filed under: General — Tags: , — m759 @ 2:42 am

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Fanciful version —

Less fanciful versions . . . 

Unmagic Squares

Consecutive positive integers:

1   2   3
4   5   6
7   8   9

Consecutive nonnegative integers:

0   1   2
3   4   5
6   7   8

Consecutive nonnegative integers
written in base 3:

00  01  02
10  11  12
20  21  22

This last square may be viewed as
coordinates, in the 3-element Galois
field GF(3), of the ninefold square.

Note that the ninefold square so viewed
embodies the 12 lines of the two-dimensional
affine space over GF(3)

As does, similarly, the ancient Chinese
"magic" square known as the "Lo Shu."

These squares are therefore equivalent under
affine transformations.

This method generalizes.

— Steven H. Cullinane, Nov. 20, 2021

 

The Lo Shu as a Finite Space

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