Published online by Cambridge University Press: 03 November 2016
One of the charms of elementary geometry is that there is no theorem so well known but that one may hope to discover improvements or at least interesting variations in the proof; and the same thing is true of the constructions.
In order to decide between variations in these it is necessary to have some way of measuring the complexity of a construction. This is done by counting the number of settings of the ruler or compass and the number of lines or arcs drawn.