How to Cut a Pizza Into 3,7 and 9 Equal Slices?

How to Cut a Pizza Into 3,7 and 9 Equal Slices?

How to Cut a Pizza Into 3,7 and 9 Equal Slices?

Suppose you are given a pizza in a rectangle shape, and you want to cut it into three equal parts, seven equal parts, and nine equal parts. Is there a way to easily do that? The blog will discuss the math behind the solution and explain how to approach this and similar problems.

A pizza can be cut into three equal slices using two parallel cuts, one vertical and one horizontal (see the first picture). The first slice contains the pizza, and the second slice contains the pizza. If we continue cutting in this way, we obtain three more slices with equal areas.

Each of these pieces can be divided into three equal portions giving us six smaller pieces with rooms. But this way, we have nine identical slices with areas. So there must be another way to cut a pizza into nine equal slices! Is there any other way to do that?

Make a Triangle Out Of Three Pizzas

The pizza triangle is a fantastic visual trick used to solve geometry problems. It is a triangle with a unique property. If you look at the image above, you will see that the pizza triangle comprises three pizzas. 

With a triangle pizza you can cut it into three equal pieces with three straight cuts without ever lifting your pizza cutter. Even as it might not appear to be much, it is a fascinating property of this triangle.

Here’s how to slice your pizza to get two triangles of similar size. You need three pieces:

  1. Grab your first slice and place it on another portion, as shown in Figure 1 below. 
  2. Next, grab your third piece of the pie (or second if you put one on top) and place it between the other two. 
  3. Repeat until you’ve built up all three layers.

Arrange The Rest Into A Straight Line

The first step is to arrange all three pieces of your pizza in one straight line. Just like how you would line up for roll call in school. The easiest way to do that is to center each piece of your pie on top of each other with their edges overlapping ever so slightly. 

This will make it easier for you to pick them up when it’s time to grab a slice. Next, divide each piece in half again: Now it’s time to separate each third section into two more equally sized pieces without cutting through any part of your pizza’s crust or outer edge.

Use The Slices To Cut Each Pizza Again

There are two ways to use your newly divided pizzas. The first is to continue dividing each one again by thirds. So, if you were to divide each of these nine new pieces by thirds (9 x 3 = 27), you’d end up with 81 little squares! And there you have it – 81 perfectly-sized bites. You could then serve them on a flat plate or arrange them onto individual ramekins that have been lined with parchment paper for easy removal. There Are Exactly Six Equal Pieces!

While math equations are sometimes tough to solve in math class, you can solve for any number of equal pieces using algebra. The trick is understanding that each fractional slice is part of a whole piece. So start by calculating how many total pieces your pizza can be cut into (8 for an 8-cut pie or 16 for a 16-cut pie). 

And after that, distribute that figure by six (this will tell you how many cuts there are) and then multiply that answer by 2 (because each whole piece will give you two of each slice). 

For example: How many 6-inch pizzas fit on one 12×18 inch pan? We know it takes four 12×12 square pans to fill one full-sized 18×18 pan. Many people have heard of the famous method of cutting a pizza into three equal slices.

The method of cutting a pizza into three equal slices is:

  1. Lay your pizza down on a flat surface
  2. Cut the pizza into two halves by drawing a straight line from one edge to the other
  3. Now, cut each of these halves in two, and you will get three equally sized, triangular slices

But what if you want to cut into nine equally sized slices? This tutorial will give you the method of doing it.

How to cut a pizza into 3,7, and 9 equal slices?

Using conventional geometry, it is not possible to cut an eight-sided figure (such as a circle) with straight cuts so that each of the three pieces has an area of exactly one-third. 

However, it is possible to achieve an approximation within 1% if more accurate cutting tools than sharp knives are used: knives with blades shaped like rose petals. 

Of course, in practice, neither knife would be perfect; for example, in each case, there will be some small area (left out by mistake) that should have been included in at least one slice.


There is an exciting and straightforward fact that you can use to cut a pizza into 3, 7, and 9 equal slices. Furthermore, the cuts must be made on the diagonal rather than the horizontal or vertical. We will consider the problem in the general case. Let’s consider the pizza in the figure below.


This is one of those mathematical problems so stated that it seems like there shouldn’t be an answer. 

For example, a flat circle with insufficient surface area to divide by three or nine seems destined to have leftover pieces. But, surprisingly (and satisfyingly), it turns out that there are many solutions. See here for a great solution and here for another excellent explanation of why you can get all three parts precisely correct.