The impossible cut: a test of judgment about weights
Balance-arm diagrams marked 2, 2, 4, and a riddle that exposes the 'sorry mathematician'
Two diagrams of a suspended balance staff carry regular unit markings—four units on each arm, paired as 2 and 2 and combined as 4—with a piece cut from one arm and re-attached at its end. The accompanying note poses a test: ask a man where to cut one of the two equal arms so that the severed piece, fixed to the end of the remainder, exactly counterweights the opposite arm. Leonardo declares this can never be possible, so anyone who supplies a position 'is a sorry mathematician.'
On this page
A balance test of true judgment
The note asks at what location one must cut one of the two equal arms of a balance so that the cut piece, attached to the end of its remainder, makes a counterweight to the opposite arm with precision—concluding this can never be possible, so whoever gives a position is a sorry mathematician.
Balance staff with cut and re-hung arm
A suspended balance staff is drawn with four units on each side; a four-unit piece is cut from one arm and appended to the end of the remainder.
Unit divisions of the arms
Each arm is divided into equal units, paired 2 and 2 and combined as 4, and the cut segment is measured against the remainder.