Megalithic Geometry: Woodhenge

Construction of an egg-shaped circle, Type I.

We illustrate the construction of Thom, 1967, Fig. 4.3, p. 29, using the outer circle of Woodhenge as an example. See Thom, 1967, Fig. 6.16, p. 74.

This construction requires (in general) a P-triple (b, c, a) and three radii, r1, r2, and r3, satisfying the conditions:

So that the P-triple may be expressed in reduced form, that is, without any common factors, we also make use of a multiplier, M. That is, all of the parameters (b, c, a) and (r1, r2, r3) are to be multiplied by M for the actual construction. For Woodhenge, M=1/2, so we will simplify the discussion by using half-yards (that is, half an MY) as the unit of length.

For all 6 circles of Woodhenge, (b, c, a) = (35, 12, 37) half-yards (i.e., M = 1/2) and for the outer circle, r1 = 24 MY = 48 half-yards. Thus

Here, then, is Thom's construction, step-by-step. The main axis is oriented to mid-summer sunrise in 1800 BC, but we show this as a horizontal line to simplify the drawings.
Step 1. We begin with the Pythagorean triangle, with the short side c = 12 on the sunrise axis, like this.
Step 2. Now double the triangle.
Step 3. Extend three sides of the figure as needed.
Step 4. Draw the large end of the egg, a half-circle of radius r1 (red) and center at the red point.
Step 5. Draw the upper side of the egg, a circular arc of radius r2 (blue) and center at the lower blue point.
Step 6. Draw the lower side of the egg, a circular arc of radius r2 (blue) and center at the upper blue point.
Step 7. Draw the small end of the egg, a circular arc of radius r3 (green) and center at the green point.
Ralph H. Abraham, 07 May 1996.