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 \(A\hat{O}B\).

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