Reconstruction of the Old Hayward Farm 20-07-2006 formation

Reconstruction of the
Old Hayward Farm 20-07-2006 formation

Draw a (small) circle. Draw and extend the horizontal and vertical centerlines.

Copy circle 1 two times, to its lefthand and righthand intersections with the hoizontal centerline. Move the lefthand circle (copy and delete original) to its own lefthand intersection, the righthand circle to its own righthand intersection (to create three tangent circles on a row).

Construct a circle centered at the lefthand intersection of circle 1 and the horizontal centerline, tangent to righthand circle 2 at the righthand side.

Construct a circle centered at the righthand intersection of circle 1 and the horizontal centerline, tangent to lefthand circle 2 at the lefthand side.

Construct a circle centered at the lefthand intersection of lefthand circle 2 and the horizontal centerline, tangent to circle 1 at the righthand side.

Construct a circle centered at the righthand intersection of righthand circle 2 and the horizontal centerline, tangent to circle 1 at the lefthand side.

Construct a circle centered at the righthand intersection of circle 4 and the horizontal centerline, tangent to circle 1 at the righthand side.

Copy circle 6 to its righthand intersection with the horizontal centerline, and move this circle to its own righthand intersection.

Copy circles 5 and 6 as one unit three times, taking the lefthand intersection of circle 5 and the horizontal centerline as a reference-point, consecutively to the rightmost intersections with the horizontal centerline (the first of circle 8, the second and third of the newly copied sets), as shown.

10.

A circle is fully defined by the two end-points of a centerline; in the following steps, such a circle will be called a 2-points circle, with references to both points.

Construct a 2-points circle, with one point at the righthand intersection of circle 1, the other point at the righthand intersection of circle 8, both with the horizontal centerline.

11.

Repeat step 10 six times, with respect to circles 9 in stead of circle 8.

12.

Copy circles 1, 5 and 6 as one unit, taking the lefthand intersection of circle 5 and the horizontal centerline as a reference-point, to the righthand intersection of the rightmost circle 9 and the horizontal centerline.

13.

Construct a 2-points circle, with one point at the center of circle 1, the other point at the center of the copied circle 1 of step 12, as shown.

14.

Copy circle 7 to the center of the copied circle 1 of step 12.

15.

Construct a circle concentric to circle 1, tangent to circle 14 at the righthand side.

16.

Copy circles 1, 5 and 6 as one unit, taking the righthand intersection of circle 6 and the horizontal centerline as a reference-point, to the lefthand intersection of circle 5 and the horizontal centerline. Repeat this three times, consecutively to the leftmost intersections of the copied circles with the horizontal centerline, as shown.

17.

Construct eight 2-point circles, the first point of each at the center of circle 14, the other points alternatively at the rightmost intersections with the horizontal centerline of consecutive copied sets of step 16, and the others at the centers of the copied circles 1 of these sets, as shown. See also details.