1. S. P. 6 Ri6rdfiin and G. Daniel, New Grange (Praeger, New York, 1964). 2. G. Hawkins, Stonehenge Decoded (Doubleday, Garden City, N.Y., 1965). 3. A. Thom, Megalithic Sites in Britain (Oxford, London, 1967). 4. G. Daniel, The Megalithic Builders of Western Europe (Hutchenson, London, 1959), pp. 111-113. 5. Actually this tumulus represents what Thom calls a type D ring, one in which the two pivot stakes are placed at one-third the radius from a, rather than at the midpoint. As Fig. 3 shows, the pivots can be kept at the midpoint of the radius if a, is allowed to move inside the design. 6. L. B. Borst, Science 163, 567 (1969). 7. The monument at Borrowston Rig requires anchor points that are placed farther apart on the circumference than the intersections made by the trisecting radii demand. In this design the circle of the smaller end arc passes through the center of the larger end arc, and the wider placement of the anchor stakes may have been made on this account. The site at Maen Mawr had anchor stakes that were closer together on the circumference. If the radial line from P2 to either anchor is taken as a hypotenuse of a right triangle one side of which is half the anchor line, then the lengths of the sides of this triangle (in megalithic half-yards) are 14, 17, and 22, which is nearly Pythagorean (142+ 172= 485e 484). 8. M. Gardner, Sci. Amer. 221, 239 (1969). 9. To mention one such consequence, with the megalithic method concentric rings, such as those found at Woodhenge, can be drawn without using any special mensuration technique. That is, a rope can be lengthened by an unspecified amount and a concentric design can be drawn at once. With a flexible compass, on the other hand, the large arc in a type II egg, for example, can be drawn without special measurement but the other arcs must be changed by x amount to remain equidistant from the perimeter of the original figure. 10. Thom presents a good argument for use of a standard length of 2.72 feet (one megalithic yard) in the construction of these structures, as well as of others in both the Old World and the New. 11. The writing of this article was supported in part by the Oklahoma State University Research Foundation.