## 23 May 2018

### Ceva's Pantograph

The Italian mathematician Giovanni Ceva ($1647 - 1734$), father of a celebrated theorem in geometry, a pantograph of vertex $P$ that will serve to trisect the angle $A\hat{O}B$. The point $O$ is fixed while the point $P$ moves on the line $PO$. As the machine is constructed such that $PR=RO=OS=SP$, $R$ and $S$ will describe a circumference.

The impossibility of the trisection of an angle by ruler and compass was demonstrated by Pierre-Laurent Wantzel in $1837$.

In the applet below, choose the radius of the circle and then move the point $R$ and verify the trisection of the angle $A\hat{O}B$.