X 0 1 2 3 4 5 6 7 8 9

0 01 04 09 16 | 36 49 64 81

1 21 44 69 96 | 56 89 24 64

2 41 84 29 76 | 76 29 84 41

3 61 24 89 46 | 96 69 44 21

4 81 64 49 36 | 16 09 04 01

I am finding it a bit more informative to look at the numbers to see all the different ways the squares relate rather than just memorizing the equations.

The symmetry is nice. It would be interesting to play with how this is changed by adding dimensions

Base 10 divides into 2 dimensions nicely.

In 3 dimensions in base 10 is it the LCD of 30 that sets the length of the series?

How about hypercubes? Is the series length 20?

It is a shame we can’t think in more than 3 dimensions. I suspect that if we could use our spatial memory these regular shapes and their relationships might be a lot easier to understand.

Has any one attempted to understand algebra geometrically (rather than, the other way around) and is there any interesting insights to be had from the effort or is it just the ravings of a newbie?