How Many Sides Does a Circle Have?

If a triangle has three sides, and a rectangle has four, how many sides does a circle have? 

This was the question posed by Ihsan this week, which really made us ponder. Many immediately yelled out "One! None!" and even "Four!" We decided that we should explore this question in more detail to try and reach some sort of conclusion.

In order to do so, the following day students were broken into small teams and given a piece of string and some stick pins. They were first asked to use the pins and the string to make a triangle. 

It was interesting to see how each group approached the task. A couple groups figured out that they could use the pins as the vertices, which helped them make the shape quickly.

The students then moved through the process of making a series of shapes, each one a bit more difficult than the one before. 

Many discoveries were found as the shapes were explored, such as when Amirah realized that a hexagon's vertices line up. Her group used this new understanding to more accurately place the pins and more successfully make the shape.

Finally, we got to the shape we began exploring in the first place: the circle. At first many students thought it was easy to make this shape, and they quickly put the pins into place. After the string was attached, however, they began to realize that their circles had short, straight sides. As Adrian explained, our circle creations weren't really circles as they weren't completely round. 

This exploration led us to discover that in order to make a completely round circle we would have to have tiny pins that we could place touching one another. The pins we had were much too big and left too much space! We realized that circles actually have an infinite amount of sides, and it was eye-opening to think about the concept of infinity. As Levi said, we could begin counting now and if we continued counting until we got so old and died, we would have to continue counting after death! 

We will continue exploring shapes throughout the next few weeks and will have many more questions to explore. Stay tuned to hear more about our discoveries!