This week I am celebrating ten years since we arrived in Zambia, so I have planned a week of ‘Ten’ words. Today’s words all have a basis in mathematics or measurement.

**decagon **(noun)

A 2-dimensional shape with ten sides

from Greek *deka *ten and *gonia *an angle

At last we reach my love of mathematics! Shapes – 2D and 3D – angles, measurements, quantities and the delight of mixing and matching. Wikipedia has this wonderful graphic to show you how to draw a regular decagon (that is one with equal length sides and angles).

As I read the Wikipedia article on the decagon I got more and more excited. Firstly, the formula for calculating the area is utterly ridiculous… and then it can be simplified to *A=2.5dt*. Why not start with this? Hmmm. Sometimes mathematicians are too precise for their own good!

Then I read that the length of a side of a regular decagon is related to The Golden Ratio. This is another mathematical concept that pleases me for its aesthetics: generally speaking, when you are looking at a rectangle that is well proportioned, that looks ‘right’ the length of the long side to the short side are nearly always in line with this ratio. It sounds utterly ridiculous, but then most paintings in art galleries fall into its trap.

Furthermore when I go on to read about the **decahedron** (the 3D version: a shape of ten faces) I begin to read about topology – a topic I studied at university. Then I realised I couldn’t remember much of it. Still, a decahedron has 32,300 topologically different forms, and it is not possible to have a regular decahedron. Probably all you need to know: dodecahedron is a much nicer word, but we’ll have to wait two more years to become engrossed in a 12-sided object!

Confusingly, I note that an Equine decahedron is a twenty-sided object: Why?!

**Decalitre **(ten litres), **decagramme **(ten grammes) and **decametre **(ten metres) bring in all the units of measurement in tens apart from time (which I looked at in Monday’s post). Liquid, weight and length can all allow their standard measures to be counted in tens. For me, I have always thought it amazing that one cubic centimetre is the same volume as a millilitre, and that (as water at room temperature) it weighs one gramme: a lovely interrelation between the measures.

And so the mathematical concepts in chunks of ten are pulled together. Tomorrow is my final day of ‘ten’ words, with a miscellaneous collection of other words.

**On Friday: miscellaneous remaining tens!**

*In the Shade of the Mulberry Tree is available for kindle from Amazon for 77p in the UK or $1.17 in the US until 22 June 2013.*