Maximizing Pieces with Cuts

Dr. Tom Crawford from the University of Oxford explains how to cut a pizza into 22 slices using six cuts, claiming it as the maximum possible. The video delves into deriving a general formula for the maximum number of pieces a circle can be divided into using n cuts. The process involves exploring small values of n, identifying patterns, and deriving a recursive relation. The formula is further explained using Gaussian sums, and a practical attempt to cut a pizza into 22 pieces is demonstrated, highlighting the challenges involved.

What is the maximum number of pieces a pizza can be divided into using six cuts?

• 22

• 20

• 18

• 24

How many pieces can you get with one cut on a circle?

• 1

• 3

• 2

• 4

What is the maximum number of pieces you can get with two cuts?

• 3

• 4

• 5

• 6

To maximize the number of pieces with three cuts, what should the third cut do?

• Intersect all existing lines

• Intersect two lines

• Intersect one line

• Avoid intersecting any lines

What is the maximum number of pieces you can get with three cuts?

• 7

• 8

• 6

• 5

What is the key to maximizing the number of pieces with each additional cut?

• Intersecting all existing lines

• Avoiding previous cuts

• Cutting at random angles

• Cutting parallel lines

How many pieces can you get with four cuts?

• 11

• 9

• 10

• 12

What is the maximum number of pieces you can get with five cuts?

• 16

• 14

• 15

• 17

What mathematical concept is used to derive the general formula for maximum pieces?

• Algebra

• Geometry

• Recursion

• Calculus

What is the recursive formula for the maximum number of pieces with n cuts?

• f(n) = f(n-1) + n

• f(n) = f(n-1) / n

• f(n) = f(n-1) * n

• f(n) = f(n-1) - n