Now, I don't know if you misphrased the question but if the pan is x% bigger than half the slice, then it would fit without cutting anything (even if it is 0% bigger and thus equal the size of the pan).

Wait...sorry, it's the area that is compared, thus the diameter won't fit into the pan...right.

The pan is x% bigger than half the area of the pizza (thus I take it you mean the area of the pan).

This is just a guess, cause I'm not that good at math, but let's say this equation would work though, because we need equal slices where the space between them exactly match each slice (so that half the pizza, gets to be full the pizza and thus if x is 100% bigger than half the area of the whole pizza then it would still fit the diameter), let's say the fewest cuts needed are: (x/100)-1.

I'm probably wrong with my equation though, but I think my reasoning is correct; if x is 100% (thus equal the full pizza) then it would fit without any cuts. But if x is smaller than that, then we need to make cuts with equal spacing so that it again fills the entire area of the pan, the cuts should be made so that the spacing + the area of the slizes makes up for 100% of the full area of the pizza.

Thanks Cyperium for your kind reply. Yes it is areas, not diameters.

I did this to avoid equations involvng Pi which cancels in a question about pizza pie.

The difficulty we have answering is the fault of Maths. Maths is very unhelpful at telling us where to start and how to think!

You have given us a great place to start - a formula.

Formulae are nice - for like diagrams you can see what the consequences are

So let's test formulae like the one you suggest:-

OK, if the round pan area is 2A then no cuts are required and our half pizza fits snugly occupying half the pan.

But if the round pan has only area A then NO SPACE WHATSOEVER will be left if and when we manage to fit area A within it. To do that will require an infinity of straight cuts just to intimately contact the curved pan boundary

So the number of cuts might be something like 1/(x/100) - 1

Perhaps that is pessimistic, for it says 9 cuts for x=10%

That COULD agree with common sense but

it says ONE more cut is all that is required for x=50%.

Does that seem reasonable to you?

The best I have managed experimentaly for a half 12" pizza is one more cut fits the two resulting pieces in an 11" pan and the two pieces differ a lot in shape.

What I find most interesting is why and HOW did such a simple question get to have an answer beyond the reach of maths and computing.