part of a circle

part of a circle
Originally uploaded by simonsterg.

When we went to the beach one afternoon I took the cord, a ring and a stick. The others watched as I staked the stick in the sand, tied the cord to the ring and put the ring over the stake so it would turn freely.
‘Dorcas, this will be easy for you,’ I said. ‘It’s the hexagon.’
Dorcas stood back from me and announced in a loud voice to the other two:
‘The amazing Leon will now create a perfect hexagon, using only circles and a straight stick.’
‘First of all we need to make the sand flat and get the stones out of the way,’ I said.
We threw the stones towards the sea and smoothed the sand out with sticks.
Then the others stood back while I walked the cord round the stake, digging a circle into the sand just as Pythagoras had done. I made the second and third circle, and then with a stick linked the points to make the hexagon.
Dorcas cheered. She made us all gather up stones and lay white ones along the three circles, and black ones for the hexagon.
After that she made the other two have a go at creating their own hexagons just as I had.
Somehow because she was excited the others agreed straight away, and not only made the hexagons, but were enjoying it as well.
‘This is a kind of game too,’ she said. ‘You have to ask yourself: Can I make a square? Can I make a pentagon? Then the challenge is to make them just using the rope and the stick.’
I’d learnt to make many shapes like this with Anaximenes, but using paper and ink. Over the next weeks the four of us made a lot of them in the sand, and carefully laid stones in the lines of sand to make them last longer. No one moved our stones. The beach became our beach, a giant scroll, its stones not scattered randomly any more but mapping out figures in circles and lines.

tyrant

It was people like Polycrates that gave us the name 'tyrant'.

The part of Aristotle's Politics which mentions Polycrates is worth quoting:

Tyrannies are preserved two ways most opposite to each other, one of which is when the power is delegated from one to the other, and in this manner many tyrants govern in their states. Report says that Periander founded many of these. There are also many of them to be met with amongst the Persians. What has been already mentioned is as conducive as anything can be to preserve a tyranny; namely, to keep down those who are of an aspiring disposition, to take off those who will not submit, to allow no public meals, no clubs, no education, nothing at all, but to guard against everything that gives rise to high spirits or mutual confidence; nor to suffer the learned meetings of those who are at leisure to hold conversation with each other; and to endeavour by every means possible to keep all the people strangers to each other; for knowledge increases mutual confidence; and to oblige all strangers to appear in public, and to live near the city-gate, that all their actions may be sufficiently seen; for those who are kept like slaves seldom entertain any noble thoughts: in short, to imitate everything which the Persians and barbarians do, for they all contribute to support slavery; and to endeavour to know what every one who is under their power does and says; and for this purpose to employ spies: such were those women whom the Syracusians called potagogides Hiero also used to send out listeners wherever there was any meeting or conversation; for the people dare not speak with freedom for fear of such persons; and if any one does, there is the less chance of its being concealed; and to endeavour that the whole community should mutually accuse and come to blows with each other, friend with friend, the commons with the nobles, and the rich with each other. It is also advantageous for a tyranny that all those who are under it should be oppressed with poverty, that they may not be able to compose a guard; and that, being employed in procuring their daily bread, they may have no leisure to conspire against their tyrants. The Pyramids of Egypt are a proof of this, and the votive edifices of the Cyposelidse, and the temple of Jupiter Olympus, built by the Pisistratidae, and the works of Polycrates at Samos; for all these produced one end, the keeping the people poor. It is necessary also to multiply taxes, as at Syracuse; where Dionysius in the space of five years collected all the private property of his subjects into his own coffers. A tyrant also should endeavour to engage his subjects in a war, that they may have employment and continually depend upon their general. A king is preserved by his friends, but a tyrant is of all persons the man who can place no confidence in friends, as every one has it in his desire and these chiefly in their power to destroy him.