- #1

Hello,

I am trying to follow an example/explanation, but with no luck. Here is the question:

Let n be the number of cuts and let a

Now it is clear that a

(Now here is the part in the example where I get confused):

Similarly, a third cut should cross both of the previous two, but not where they cross each other. This yields a

How did they do that? I don't understand. Wait a minute, I think I do understand how they did it. But, the pieces couldn't be equal could they? Is it possible to make three cuts, get seven pieces, but have all seven pieces equal?

The example goes further:

Suppose n - 1 cuts have been made and a

a

a

Ok. I didn't understand this part. Could someone reword this for me if it isn't too much trouble? I can't see what they are saying as of yet.

Any help is appreciated. Thankyou.

I am trying to follow an example/explanation, but with no luck. Here is the question:

What is the largest number of pieces you can get by cutting a pizza with n straight vertical cuts if the pieces are not to be moved between cuts?

Let n be the number of cuts and let a

_{n}be the maximum number of pieces.Now it is clear that a

_{0}= 1 and a_{1}= 2. Since we want to maximize the number of pieces, we ensure that two cuts cross. Hence, a_{2}= 4.(Now here is the part in the example where I get confused):

Similarly, a third cut should cross both of the previous two, but not where they cross each other. This yields a

_{3}= 7.How did they do that? I don't understand. Wait a minute, I think I do understand how they did it. But, the pieces couldn't be equal could they? Is it possible to make three cuts, get seven pieces, but have all seven pieces equal?

The example goes further:

Suppose n - 1 cuts have been made and a

_{n - 1 }pieces are obtained. As before, the n-th cut should cross each of the others at distinct points. Hence there will be n - 1 points of intersection on it, dividing it into n segments. Each segment cuts an existing piece into two. Hence we get the recurrence relationa

_{n}= a_{n - 1}+ n, 1 <= na

_{0}= 1.Ok. I didn't understand this part. Could someone reword this for me if it isn't too much trouble? I can't see what they are saying as of yet.

Any help is appreciated. Thankyou.

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