The broken-segment solution described in the text (cf. p. 42), in which the area of revolution is only that of the end circles of radius y1 and y2, respectively, is known as the goldschmidt solution. for the symmetric situation discussed in exercise 7, obtain an expression for the ratio of the area generated by the catenary solutions to that given by the goldschmidt solution. your result should be a function only of the parameters k and α. show that for sufficiently large values of α at least one of the catenaries gives an area below that of the goldschmidt solution. on the other hand, show that if α = α0, the goldschmidt solution gives a lower area than the catenary.