Using compass and straightedge, we can construct the midpoint of a line segment, and we can easily divide a line segment into, say three equal parts. The question is, is it possible to do these constructions

**with just the compass**.

The answer is "yes"! Indeed, it is possible to construct the midpoint of a line segment, and it is possible divide a line segment into a number of equal parts by using the

**compass alone**. How amazing is that?! Today, we will look at these constructions!