# Twelve

### More bits about the number twelve

There are twelve months in the year, divided roughly into 4 seasons; twelve signs of the Zodiac, divided into 3 sets of 4 each; and twelve hours, reapeated through each day and night.
If we use base twelve to count these hours then four am, for example, is 4 o'clock, and 4 pm (twelve hours later) is *14 o'clock.

Twelve is divisible by the sum of its digits and by their product.
The sum of the proper divisors of 12 is 12^{2} = 144; written in base twelve this becomes *100.

There are twelve tones in the modern twelve-tone musical scale; in the equally tempered scale the step from one tone to the next is the twelfth root of 2.
Twelve identical spheres can touch one other such sphere, each of the outer spheres touching the central sphere and four others.

Twelve is the first **abundant number**, it is less than the sum of its factors excluding itself:

1 + 2 + 3 + 4 + 6 = 16

There are only twenty-one abundant numbers not greater than 100, starting 12, 18, 20, 24, 30, 36 ...

More like this can be found in **The Penguin Dictionary of Curious and Interesting Numbers** whence I took some of the above.