King of the Hill
Last night, szym.net and I were thinking about great places to live. Cambridge is wonderful, but sometimes, you have to go and fly around a bit. We didn't actually reach any conclusion but we did ask ourselves a few questions.
Should we live on the top of a ski slope? Yes.
But there would be too many people and all the ski lifts would end right in front of our house. And given the price of land, we would only be able to afford a small chunk.
But! If we bought a ring of land ...
Formula for buying land on a hill assuming there's no need for a thickness to your ring:
Q = All the money you have
p = Price of square footage
a = Area of your house (not including the backyard)
r = Radius of circular plot of land you can fake to have = (Q-P*a)/(2*\pi)
Total effective area you get to be king of:
A = (\pi*r^2)
Let's look at the numbers:
If you have Q = $100 and the price of square footage was p = $10, you would typically only afford 10 sqft of land at the top of the hill. Let's say your house takes up a = 5 sqft. Plug the numbers in and instead, you could pretend have a circular plot of land with radius r = (100-10*5)/(2*\pi) = 7.96 ft. That means, now, instead, you can have A = (3.14*7.96*7.96) = 200 sqft. to enjoy!
10 sqft => 200 sqft
