Under Phillip Augustus beginning in 1190, Paris enclosed approximately one square mile in 20 foot walls 10 feet thick. It took about 25 years for a city of 30,000 people. Just saying!
We've got WAY less than 30,000 people. I'm not sure if we have [sqrt 3*(10^4)] people yet!
...[(sqrt 3)*(10^2)] is actually about how many people live in our town. Huh.
Anyways, that's convenient. Assuming our cities are in the same shape, our city's area would probably be about the square root of Paris's (assuming no room for growth was added), which would mean the wall was...let's see. For the sake of calculations, assume a square wall; the ratios should work out the same using whatever shape, but squares are easiest.
p
P=4s
PA
P=s
P2p
s=4s
sA
s=s
s2A
P=A
s2s
P2=s
s4s
P=s
s2This doesn't sound right...I'm almost certain I made an error somewhere...
[MATHS REDACTED]
It would take 3.2 years.
Huh. This works out better. Let's go with 3 years, 2 months, and 12 days. Make it "and 2.5 months"--those extra few days will help us if something unexpected goes wrong.