A perplexing pizza problem...

[sawyl]

Got into a discussion about pizzas and value for money with someone who was, I suspect, deliberately pretending to be innumerate to wind me up. The conversation went somewhat as follows:

Them:	We always get two 12" pizzas and end up talking half home. I can't understand why people buy their 16" ones. They cost twice as much, but you're only getting 16 inches of pizza instead of 24...
Me:	[ boggling ] I'm not sure it works like that...
Them:	[ blithely ] ...people are always really impressed when I tell them that... It's much better value for money
Me:	But the area varies with according to the square of the radius... [ estimating frantically ] So if we say that a 16" pizza is around 200 square inches and a 12" is around 100, then it's going to be a pretty close run thing. Two 12 inchers are probably better value, but not by very much — certainly not double.
Them:	Really? I'll have to remember not to tell people who are good at mental arithmetic...

Having had time to run the numbers, I've realised that my rough numbers were right and my interlocutor was correct, but only just: if the costs of the larger pizza are exactly double (which, it turns out, they're not) you get 12.5 per cent more by buying two smalls; which in other terms, means that you ought to be getting a 16.9" pizza for your money (or 16.5" if the larger prices are only 1.9 times the price of a 12 incher).

As the days pass, my life feels like it's asymptotically approaching XKCD...