Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal (45 degree cuts) through any point inside the square?
If you could give an explanation as well as an answer I'd be very grateful! I'd like to learn how to do this, not just get an answer.
Draw a picture of this problem. You'll have 8 pieces, which divides evenly between two people.
http://www.scetv.org/education/ntti/images/2006/funtastic_clip_image006.jpg
Thank you! Just to make sure I'm getting the best answer, here is a hint I was given, if it helps:
The center is an obvious point where it works. What are other obvious points? For a non-obvious point, how could you determine a way to see if the pieces can be divided equally?
Would you try to find the area of each piece? If you found the area of each piece and added them up, I believe this would be a way to tell if the cuts allowed an even amount for each person.
Sure! I'd be happy to explain and show you how to share a square pizza equally between two people using four cuts. Here's the step-by-step process:
Step 1: Start by placing the square pizza on a flat surface.
Step 2: Make the first cut from one corner of the square to the opposite corner, creating two equal-sized triangles. This is the diagonal cut.
Step 3: Now, make the second cut perpendicular to the first cut, starting from the midpoint of one side and ending at the midpoint of the opposite side. This is the horizontal cut.
Step 4: The third cut is another diagonal cut, but it starts from a different corner than the first diagonal cut. This cut goes from one corner to the midpoint of the opposite side.
Step 5: Finally, the fourth cut is a vertical cut, going from the midpoint of one side to the midpoint of the opposite side, perpendicular to the second cut.
By following these four cuts, you will end up with eight equally sized pieces of the square pizza. Each person can then have four pieces, ensuring an equal share.
To visualize this process, you can imagine dividing the pizza into four equal sections by first cutting it diagonally and then making two additional cuts perpendicular to each other.
So, to summarize, you can share a square pizza equally between two people by making four cuts: two diagonal cuts, one horizontal cut, and one vertical cut.
I hope this explanation helps you understand how to achieve equal sharing of a square pizza.