Question

Use the Spider Tool to make regular polygons with more and more sides - 10 sides, 20 sides, 30 sides, and more. What do you notice about the shape of the regular polygon as the number of sides increases?

Answer 1

As the number of sides in a regular polygon increases, the shape becomes more circular, due to the sides shortening and the shape smoothing out.

Step-by-step explanation:

When using a Spider Tool to make regular polygons with increasing numbers of sides such as 10, 20, 30, and beyond, one will notice that the shape of the regular polygon begins to approximate a circle. As the number of sides increases, the individual sides become shorter and the shape becomes smoother, causing the polygon to look more and more like a circle. This is due to the fact that a circle can be thought of as a regular polygon with infinitely many infinitely small sides.