But geometry furnishes the best sport. Here is a learned American archæologist, Mr. Jay Hambidge, lecturing to that august body the Hellenic Society and revealing to them his discovery that the secret of classic Greek art (of the best period) is a matter of two magic rectangles. I understand that the learned gentleman himself did not make this extreme claim about the “secret” of “Art,” but it was at any rate so described in the report on which my remarks are based. Mr. Hambidge appears to have devoted years of labour and ingenuity to his researches. The result is in any case of curious interest. But how that result can be said to be “the secret of Greek art revealed” I wholly fail to see. Let us look first at his rectangles. His first is 2 × √5. It is said that these figures represent the ratio of a man’s height to the full span of his outstretched fingers. But what man? Of what race and age? Well, let us say an average Greek of the best period, and pass on. Mr. Hambidge has found this rectangle over and over again in the design of the Parthenon. “Closely akin” to it, says the report, is another fundamental rectangle, of which the two dimensions are in the ratio of Leonardo’s famous “golden section.” That ratio is obtained by dividing a straight line so that its greater is to its lesser part as the whole is to the greater. Let us give a mathematical meaning to the “closely akin.” Calling the lesser part 1 and the greater _x_, then— _x_/1 = (_x_ + 1)/_x_ or _x_² - _x_ - 1 = 0 which gives you _x_ = (√5 + 1)/2. The square roots will not trouble you when you come to constructing your rectangles, for the diagonal of the first is √(5 + 4), or 3. If AB is your side 2, draw a perpendicular to it through B, and with A as centre describe the arc of a circle of radius 3; the point of intersection will give C, the other end of the diagonal. The second rectangle maintains AB, and simply prolongs BC by half of AB or 1. Just as the dimensions of the first rectangle are related to those of (selected) man, and to the plan of the Parthenon, so those of the second are related, it seems, to the arrangement of seeds in the sunflower and to the plan of some of the Pyramids. Sir Theodore Cook writes to _The Times_ to say that both the sunflower and the Pyramid discoveries are by no means new.