If you cut a pizza into 45 degree wedges meeting at a point other than the center and two people eat alternative slices, do they each get the same amount?
Surprisingly, if you make 4 slices, the answer is no. But if you make 8 slices as wanted, the answer is yes. A google search on "pizza 45 degree slices" turns up a book on google books named "Which way did the bicycle go?"
It contains a nice article which shows that you can use calculus and polar coordinates to prove it.
To determine if two people would get the same amount of pizza when eating alternating slices of a pizza cut into 45-degree wedges, we can use some mathematical reasoning.
First, let's visualize a pizza cut into 45-degree wedges meeting at a point other than the center. Each slice will have the same angle, but their widths might differ. The total number of wedges formed depends on the number of times the wedges meet at the center.
To calculate the number of times the wedges meet at the center, we can use the formula:
N = (360 / θ) - 1
Where N is the total number of wedges and θ is the angle between the wedges.
For example, if the angle between the wedges is 45 degrees:
N = (360 / 45) - 1
N = 8
So, there would be a total of 8 wedges created.
Now, let's consider two people eating alternating slices. If there are 8 wedges, person A would start with one slice, and person B would start with the second slice. They would continue taking turns until all the slices are consumed.
Since both people are eating one slice at a time, and there are an equal number of slices for each person to start, they will end up with the same number of slices. Therefore, assuming the pizza is cut exactly into 45-degree wedges meeting at a point other than the center, both people would get the same amount of pizza.
It is worth noting that if the pizza is not cut precisely into equal 45-degree wedges or if the shape of the pizza is irregular, the result may vary.