Mathematics — Number Theory · continued-fractions-rectangle-decomposition
Problem
(a) A rectangle with sides of length 13 and 48 can be partitioned into squares in the way shown in the figure. Determine the lengths of the sides of all the squares, and relate the numbers of squares of each size to the continued fraction for 13/48.
(b) Draw the analogous figure decomposing a rectangle of sides 19 and 42 into squares, and relate this to the continued fraction for 19/42.