Mohr–Mascheroni theorem

In Euclidean geometry, the Mohr–Mascheroni theorem states that any geometric construction that can be performed by a compass and straightedge can be performed by a compass alone.

This theorem refers to geometric constructions which only involve points and circles, since it is not possible to draw straight lines without a straightedge. However, a line is considered to be determined if two distinct points on that line are given or constructed, even if the line itself is not drawn.

Although the use of a straightedge can make certain constructions significantly easier, the theorem shows that these constructions are possible even without the use of it. This means the only use of a straightedge is for the aesthetics of drawing straight lines, and is functionally unnecessary for the purposes of construction.