Trisecting the Angle/Fallacious Proof/Edw. J. Goodwin

Fallacious Proof of Trisecting the Angle

The trisection of a right line taken as the chord of any arc of a circle trisects the angle of the arc.

-- Edw. J. Goodwin

Resolution

Basically this says $\sin x = x$.

Make the angle large.

Draw a $135 \degrees$ arc, so that trisection is obviously at $45 \degrees$ and $90 \degrees$.

Observe that the middle piece of the chord is too short for the chord to be trisected.

$\blacksquare$

Sources

• 1895: Edw. J. Goodwin: Queries and Information: (A) The trisection of an angle (Amer. Math. Monthly Vol. 2, no. 11: p. 337)  www.jstor.org/stable/2971569