Fortnightly maths prize for 24 February

No prize-winners this time. Though I know (because they told me) that the year 13 Further Maths students worked out answers, none of them wrote down the answers and handed them in, so no prizes.


If all the people of the world stood shoulder-to-shoulder (with the babies in slings, and the old and sick people held up by the people next to them), how much area would we cover?

One estimate (from National Geographic) is that we’d cover about the surface area of the city of Los Angeles, 1300 km2. The year 13 further maths students got about the same figure.

I make it a bit less. The average-sized person can stand in an area about 0.4m×0.25m, or 0.1m2.

Multiply by seven billion, and get 7×108m2

Or 7×102km2, or 700 km2

That is roughly the area of Singapore, and a bit more than the area of Mumbai, 600 km2. London is about 1500 km2, and so is Sao Paulo. New York City is about 1200 km2. Brisbane is about 1400 km2, and the contiguous urban area round it (Brisbane plus Ipswich plus Logan) is about 3600 km2.

Tokyo is 2200 km2. Istanbul is over 5000 km2.

Dhaka, reckoned to be the most densely-populated big city in the world, is about 800 km2.