In the previous section, I described the chain of reasoning which led to the surprising conclusion about the nature of the geometry in the landscape around Rennes. The key insight was the discovery that on the 1:25,000 scale map of the district, the geometry is found to be laid out in units of inches. This suggested an intriguing possibility: could it be that this was the original scale of the "plans" for the landscape geometry?

If this were so, I reasoned, then it should be possible to construct the "map" as a piece of geometry, using only the allowed tools of the ancient geometer, the straightedge, compass and right-angle. To this must be added one "magic ingredient": a ruler marked in whole numbers of inches. Eventually, I was able to find a sequence of geometrical steps which did indeed meet these criteria. This method is robust, straightforward, and self-calibrating. It enables the geometer to quickly construct a geometrical figure at correct size which gives the positions of numerous key churches and other features in the Rennes landscape.

The result is a perfectly accurate, 1:25,000 scale map of the district. It is based around a grid of 18 by 19 inch squares which is offset to the vertical by a simple whole number gradient (namely 3:10). Key angles and positions in the geometry are generated by joining particular grid points. For example, a 36 degree angle is readily created by joining points which are separated by 8 squares in one axis, and 11 squares in the other. (This is simply because the inverse tangent of (8/11) is virtually equal to 36 degrees). There are various other results similar to this which the use of such a grid system permits the geometer to exploit.

The following figures give step-by-step instructions for drawing the first stage of the geometry. This includes the "circle of churches" and the "Wood pentagram", both of which were (re-)discovered by David Wood and discussed at length in his books and those of Henry Lincoln. The final figure shown below shows that the Wood pentagram does not by any means exhaust the geometry on display, and that the grid may be used to generate additional layers which account for the position of many other churches and local features, besides the ones shown here.

Figure One: The First Steps: The "Paris Zero Meridian" and the "Sunrise Line"

Figure Two: The 18 by 19 grid

Figure Three: The mr line through (11,-7) and (3,4)

Figure Four: The "Bugarach Baseline"

Figure Five: The "Circle of Churches": locating the centre and the radius

Note that the radius of the circle is derived directly from the hypotenuse of a 6 inch 36 degree right-angled triangle.

Figure Six: Drawing the "Circle of Churches"

Figure Seven: The 45 degree line through "St Just-et-le-Bezu"

The line drawn in this figure has a slope of (13,7) relative to the grid. This corresponds to an angle of 28.301 degrees (i.e. inv-tan (7/13)=28.301) If this figure is added to the (3,10) slope of the grid relative to the horizontal (or 16.699 degrees), the result is 45 degrees neat. Hence this line is at 45 degrees to the Paris Zero meridian.

Figure Eight: The "Wood pentagram" completed

Figure Nine: Beyond Wood: the location of Arques Chateau and Alets-les-Bains

It may be noted that the angle formed at Arques Chateau by the two lines shown in Figure Nine is precisely 36 degrees. This may be taken as indicating the presence of another pentagram related to the Wood pentagram. Details of this figure are held over for a subsequent posting.

Figure Ten: The Signature of the mr triangle in the location of Coustassa

The location of Coustassa is determined on the circumference of the circle of churches by a 6"mr triangle placed upright at the circle centre as shown.

Related Pages:

The Eighteen Royal Cubits: The Giza/ Rennes connection

Grid Construction of the regular heptagon

Hidden Geometry in Art:
Pierro Della Francesca:
Fra Angelico 
Fra Luca Pacioli
Denderah Zodiac

Geometrical Analysis of the East Meon Crop Circle