Duodenum: Wikimedia Commons image |

*undecim*,

*duodecim*,

*tredecim*. . . for 11 and 12 and 13.

The Latin form of 12 turns up in some unexpected places. For example, in music, a duodene is a group of twelve notes, though even the specialist musical references are unlikely to reveal this, for it is a forgotten idea, yet even people who have no idea where the duodenum is, will know that a duodenal ulcer is no fun at all. Luckily, though, we have just one duodenum, not twelve of them, to ulcerate.

In fact, the duodenum is a short section of the small intestine, immediately after the stomach, having a length of about twelve fingers' breadth, or in medical Latin, duodenum digitorum. The duodenum becomes the jejunum which takes its name from the Latin word for 'fasting', which seems a strange name to give any part of the gut, but there you have it.

After the jejunum comes the ileum, which opens into the caecum, at which point we have reached the large intestine, and strayed back into English body bits for a moment.

The Greek word for 12 was

*dodeka*, so we also run into terms like 'dodecagon', and 'dodecahedron'. The dodecagon is in the same series as the more familiar pentagon and hexagon, but having 12 sides, while a dodecahedron is in the same grouping as a tetrahedron, a solid with 12 faces and 12 angles.

The dodecahedron may be a regular figure, composed of 12 identical regular pentagons, or it may be a figure of great interest to the crystallographer, the rhombic dodecahedron.

This was first commented on by the astronomer and mathematician Johann Kepler in a moment when he left the planets alone, and it is the form that squashable spheres take up when they are packed closely together. This has twelve faces, each of which is a 'squashed square', or rhombus, each rhombus having two angles of 109.5 degrees, and two of 70.5 degrees.

The regular dodecahedron makes a reasonable approximation of a sphere, when it is made of stretching material like leather or felt and stuffed with rags or inflated with air under pressure, but it is hardly good enough for making a soccer ball. A neatly made regular dodecahedron can be used in games of chance where you need to roll a value between 1 and 12 with equal probabilities (with two cubical dice, the middle numbers, 6, 7 and 8, turn up far more often than extreme values like 2 and 12, and there is no way at all to throw a 1).

We are all familiar with decimal number systems, based on the powers of 10, and most people know about binary numbers, based on 2, because they are widely used in computers, and some people will know about hexadecimal numbers, also used in computing, and based on the value 16. A few historians of computing may be familiar with octal numbers, based on 8, because computer output in the early days was sometimes given by three lights, counting from 0 to 7.

Those of us who know our number systems really well are probably the only ones familiar with duodecimal numbers based on 12. In this sort of system, the numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, where '10' means one complete set of twelve and no units. This system has sometimes been urged by the technically competent, because a 12-piece set can be divided in more ways.

That may make sense to technicians today, but why would the Romans bother? In part, it seems, for the same reason. The Romans found it convenient to divide things into twelfths, because then you could share evenly between 2, 3, 4 or 6 people.

And as we have seen, the Romans even had a special word for a twelfth part,

*uncia*, which gave us our words for both inch and ounce. And don't laugh — the fact that our numbers don't really start a new cycle till 13 indicates that our own ancestors must have had a similar view.

A note to myself: somewhere, I have a "net" for making rhombic dodecahedra out of paper. This is a set of 12 rhombi with the correct angles, and small tabs to glue the bits together. When I find it, I will scan it and put it on the web with a link here.

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