An Incorrect Method of Constructing Pavimenti

Some authors refer to a way of pavimenti construction called the “2/3 method”, which was in used by painters till about 1435.  We will now see why it is incorrect.  In Fig. 22, the distance between the ground line and the first transversal is taken to be l.  The distance between the first and second transversal is then (2/3)l.  It follows that the distance between the n-th and the (n+1)-th transversal is (2/3)nl.  However, one only has to join the diagonals in all the grids to observe that the method is incorrect, as the diagonals formed is curved.

Fig. 22 – The “2/3 method”