Mathematics provides us ways to think about number, shape, sets, and much more. For amateur mathematicians interested in exploring its variety, I would highly recommend *The Book of Numbers* by John H. Conway & Richard K. Guy.

Over the years I’ve been drawn in particular to three aspects of mathematics.

- I thought “
**balanced ternary**” numbers to be an original idea until I found that it is mentioned in Volume 2 of Donald Knuth’s*Art of Computer Programming*, which I’d read for a college course. Dr. Knuth and I believe balanced ternary numbers to have a natural beauty not expressed in binary, decimal or other-based numbers as they’re normally expressed. **N-grams**is the name I give to an exploration triggered through exploration of the math behind the enneagram. The third drawing [of the seven across the top of this blog (mid 2010)] is a representation of the enneagram with what’s usually a triangle expressed as three points to reflect the underlying mathematics.**Dimensionalities**is the term I take to explorations triggered from studying Buckminster Fuller into the coordinate systems “indigenous” to the Platonic solids and related objects.

Two of these, balanced ternary and dimensionalities tie into ideas around measurement and accuracy that are not fully expressed here.

In searching the web for “balanced ternary” I came across the following image, titled “Generalized Balanced Ternary” – a way to capture positional information for 2 dimensions using a single number (using digits 0-6) mapped onto hexagonal patterns. I explored something quite similar decades ago. I think the Vector Equilibrium (VE) – or its dual, which (I think) is a space-filling shape – might be used to encode 3 dimensions in a single number (using digits with values 0-12) in a similar manner. It would be interesting to use a zero-centered notation for these values (digits -3 to 3 for hexagons, -6 to +6 for VE-based pattern).

None of these are subjects for cocktail conversation. Few others are interested in even thinking about understanding such mathematical esoterica. Perhaps you’re one of the few – if so welcome. Make a cogent comment.

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