How do you share a pie? You roughly estimate the slices needed and use a bit of geometry to get equal slices. What if the slices shouldn’t be equal? One gets less because she’s on diet; one gets more because she’s hungry. You re-estimate the slices according to the new conditions. The same goes with sharing land: some geometrical knowledge and a set of rules.

GEOMETRY + RULES = LAW

### Squares and Power

Squares and rectangles have been used to regulate land sharing since ancient times. It seems that the right angle has been associated more to authority and power (What can you do with a rectangle? Empower!) than the curve, perceived as egalitarian (recall King Arthur’s round table).

The right angle somehow won. Why? It might have yield more precise land measurements in a time when the area of circle wasn’t as easy to measure as today. Remember that a circle’s area depends on the radius and a strange number π whose digits never end  3, 1416…  Although π has been approximated by Babylonians to 3 (that is some 3,500 years ago) and by ancient Egyptians to 3,16, it may have rendered less exact measurements than those of a square area. Besides, dividing land along curved shapes would be too thriftless: the leftovers between circles get wasted.

Whatever the reason to choose the right angle, the puzzle is still there: why the right angle from all the possible angles at hand? It may have something to do with our vertical position? Or with a search for order (but why do we link order to the right angle)? Straightforward to measure right angles was surely not. Take a look here at the ancient method:

### How the square won over the circle: The Ancient Chinese 9-in-1 matrix

The history of the Chinese 9-in-1 matrix (the tic tac toe square is such a 9-in-1) embodies the story of organizations. One begins by being a crowd and ends up by being an organized group with a leader and a hierarchy:

Long – long time ago, some 7,000 years ago, on a plain along the Yellow River, people settled in groups in round pit-houses. The Banpo settlement, somewhat east of today Xi’an city, was an oval-shaped moat enclosing 200 round pit-houses.

Everything was round in Banpo: the village, the houses, the roofs, the sun and the sky. The 3 feet (1 meter) underground holes were safe and warm to sleep in and to store the food. But they were just an all-in-one one room apartment, that is kitchen+dining-room+bedroom+storage.

I know: bathroom is on the tip of your tongue. But the missing space is not the bathroom: it is the extra space for guests and large gatherings. Where to celebrate the beginning of springtime, to hear stories, to sing along with others? A Great Hall, close to the round pit-houses is needed. This is how the city life has started: with buildings fit for various purposes not just for dwelling.

One thousand years people in Banpo enjoyed roundness. The only square they imagined was the earth. We know this because archaeologists found pottery on which a 9-in-1 matrix (the earth) is inscribed in a circle (the heaven).

Suddenly (as sudden as can you expect something to occur after 1000 years), athletic warriors led by a brave landlord came from the East and invaded Banpo. It seems that they liked the serenity, myths, and rituals they found since they settled there and assimilated  — in other words: took as their own – parts of the local culture.

The newcomers built square cities surrounded by square walls which enclosed square houses. In rural areas they used the square (9-in-1 matrix ) to share the crop. How? A matrix corresponded to 8 farmer families. Each family would work one outer square and enjoy privately the crop. The central square would be worked together by all 8 families and the crop given entirely to the lord. The 9-in-1 matrix stratified thus the society in farmers, landlords and the emperor. How far can one go with just a square!