Niven, Quam, Cola

(Extracted from http://wiki.mindcloud.org/wiki/Niven%2C_Quam%2C_Cola ;-D)

[edit] A Story

Many moons ago, Aurgi and myself were in the awful habit of creating gratuitous pointless theoretical and mathematical systems. One of these was the exploration of different number bases. For the sake of uselessness, the number 13 was chosen to base a number system off of - at the time it seemed like a fairly obtuse number.

In order for this to work, we had to invent three new numbers (in decimal, or base ten, there are only the ten single-digit symbols: we needed three more). While convention would dictate that we use A, B, & C to be the base-13 equivalent of decimal 10, 11 and 12, we decided to ramp up the mystery and obscurity by making up three new symbols.

These were:

NIVEN - decimal value 10

QUAM - decimal value 11

COLA - decimal value 12

We imagined, with some hilarity, a whole classroom reciting the times tables in base-13: once niven is niven, two nivens is seventeen..., which led us to begin constructing a multiplication table. However, at this stage, neither of us had the mathematical knowledge to do this efficiently, so the project was shelved. It was only after two years had passed, that while converting decimal to binary, I learned the bit of knowledge that would enable the quick construction of a base-13 multiplication table. This was done immediately. The result is below: