The Maths of cities


Bacteria growing in a bottle

This little exercise gives you a feel for exponential growth and what it means to resource availability. To get the basic idea try this. Given: a bacteria in a bottle of substrate fills the bottle in one hour, starting from one bacteria. The bacteria divides every minute. Calculate: how full is the bottle at 59 … Continue reading

How much land per person

At present some 11 percent (1.5 billion ha) of the globe’s land surface (13.4 billion ha) is used in crop production (arable land and land under permanent crops). This area represents slightly over a third (36 percent) of the land estimated to be to some degree suitable for crop production. The fact that there remain … Continue reading

Round walks as teaching tools


The horse and oat cart challenge

I maintain that this little problem will illustrate how the maximum size of a city is well below that experts currently state. In fact, this problem shows that without fossil fuel the sizes of cities will be severely restricted. This little problem sets a benchmark for how large a city can be, as it is … Continue reading

The horse and oat carts problem

Although horses eat grass, they need oats. Imagine then a horse carrying food from the area of production to the city where the oats will be consumed. The driver feeds the horse the oats from the cart. Is there a way the answer to this problem could illustrate for us the maximum size of a … Continue reading

City density

An average city in Europe may show a population density of about 5000 inhabitants per km2. City centres have much more, from 12,000 upwards. However, around 40% of the area of these cities is allocated to car transport system – for example, roads, garages, parking spaces, car showrooms, repair shops and so on. If the … Continue reading

If all the world lived in one city… how big would it be?

Given the population of Earth is 7 billion And that the density of cities ranges from Mumbai – nearly 30,000 per square km Through Sao Paolo at 9,000 Through London at 5,000 ┬áto Copenhagen at 1,800 How much space would be needed for these different variants? For inspiration see the website PER MILE. For the … Continue reading

The land use of cities

Given a large city of one million. Given that the agricultural land needed to feed a family of four is about one hectare. Given that only about 30 % of land can be farmed. Given that the population density of cities can be around 5000 inhabitants per square kilometre. Calculate: If the city is circle-shaped, … Continue reading