Gauss did not find the sum of the angles different from two right angles because his measurements were not sufficiently precise. If they had been much more rigorous, or if he could have used a much larger triangle—with the earth, Jupiter in opposition, and another planet as its apices—he would have found a considerable difference. The real universe is not Euclidean. It is only approximately Euclidean in those parts of space where light travels in a straight line: that is to say, in the parts which are far from any gravitational mass, such as that in which, on an earlier page, we left Jules Verne’s projectile. There are many other reasons why the universe, in consequence of gravitation, does not conform to the laws of Euclid’s geometry. For instance, in the Euclidean geometry the extent of the circumference has a well-known proportion to its diameter, and this is indicated by the Greek letter π. This proportion, expressing how many times the diameter is contained in the circumference, is equal to 3·14159265 ... etc., but I pass over the rest, as π has an infinite number of decimals. We then ask: In practice is the proportion of circumferences to their diameters really equal to the classic value of π? For instance, is this precisely the proportion of the earth’s circumference to its diameter?[11] Einstein says that it is not, and he gives us the following proof. Imagine two very clever and quick and wizard-like surveyors setting out to measure the circumference and diameter of the earth at the Equator. They both use the same scales of measurement. They begin measuring at the same moment, and they start from the same point on the Equator. But one goes westward and the other eastward, and their speeds are equal, and such that the one who goes westward keeps up with the earth’s rotation, and thus sees the sun all day long stationary at the same height above the horizon. In music-halls, for instance, one sometimes sees an acrobat walking on a rolling ball and keeping to the top of the ball, because the pace of his steps is exactly equal and contrary to the displacement of the spherical surface. [11] We are, of course, imagining the earth as perfectly circular, without irregularities. A stationary observer in space—on the sun, let us say—would thus see our surveyor who is going westward, stationary right opposite to him. On the other hand, the surveyor who goes eastward will seem to him to go round the earth, and twice as quickly as if he had remained at the starting-point.