The ground plans on this page are drawn based on:
- Bronneger D22 - excavation plan, van Giffen [6.1] *)
- Bronneger D25 - eigen metingen (geïdealiseerde versie)
- Drouwenerveld D26 - own measurements
- Emmen D38 en D39 - own measurements
- Emmen D40 - excavation plan, van Giffen [6.2]
- Heveskesklooster G5 - excavation plan, Lanting [6.]
- Mechelsdorf 12 **) - own measurements
- Barkvieren 92 - own measurements
- Serrahn 540 - excavation plan, Schuldt [6.4]
- Serrahn 541 - field plan, Schuldt [6.5]
- Frauenmark 632 - own measurements
- Bourbouillet - field plan, Chevalier [6.6]
- Bougon F - field plan, Chevalier [6.7]
- Grammont 1 - field plan, Chevalier [6.8]
- Gouziac-S - field plan, Chevalier [6.9]
- Pichouno - field plan, Chevalier [6.10]
*) As a result of own measurements the excavation plan must be turned a few degrees.
**) The numbering of the dolmens in Mecklenburg follow the system of Schuldt.
On this page field plans are used for Serrahn 541 and the French dolmens.
Since in general this type of plan gives a less reliable representation, a justification should be made here.
Serrahn 541 no longer exists. Its field plan comes from Schuldt. When comparing own measurements of still existing dolmens with the concerning field plans of Schuldt, they agree well. Most small stones are depicted a little too big and the entrances stand on a deviating angle to the chamber now and then. Both we don’t find in Serrahn 541.
The field plans of the French dolmens is the work of Chevalier. Hoskin writes about him: "Yves Chevalier was meticulous in the extreme" [6.11]. Hoskin, as an astro-archeologist, places this remark in consideration of the preciseness of the orientations, which apparently he feels is lacking with other acheologists.
For a matter of fact, no new patterns are introduced on the basis of field plans (in accordance with the demands on the page Accounts). The concerning patterns are found with other monuments and the field plans are used to present variations only.
Dolmen D22 has some striking features. Side stone S2 has its flat side at the outside instead of the inside of the chamber. The longitudinal walls of the chamber contain at one side three stones but at the other side two. Because of the concatenation of trilithons hunebedden normally have the same number of stones in the opposite walls. Two of the three side stones (Z1’a and Z1’b) were taken for one at first glance by van Giffen. Only during excavation it appeared that the hunebed had two stones instead of one in this place. Because of the small distances between the side stones D22 looks a little like an enlarged dolmen.
During a quick survey of the ground plans of dolmens in Mecklenburg, it appeared there was a similar plan to that of D22: Serrahn 541. There is no excavation plan available for Serrahn 541 and during the unification of East and West Germany the dolmen has been cleared away by the landowners . Regrettably we cannot have a detailed plan for this dolmen anymore. The chambers of D22 and Serrahn 541 have the same outline, but differ in their sizes. In D22 the gap in the strange double stone Z1' falls together with a deviding wall in Serrahn 541. Besides this, the outside of side stone S2 stands at the same oblique line as the inside of the comparing stone in Serrahn 541 (blue arrows in figure I below). Later on the same chamber pattern was found with the only Dutch dolmen (G5) and two other dolmens in Mecklenburg. The end stone in Heveskesklooster G5 has the same obliquity as the ones in D22 and Serrahn 541 (figure II). In both other dolmens of Mecklenburg it’s the threshold, which stands along that oblique line (figure III). With its end stone and threshold, Serrahn 541 seems to play a double role. The pattern mirrors itself in the ground plan: on one hand like D22 with the end stone (figure I) and on the other hand like the enlarged dolmens with its oblique threshold (figure III).
The uniformaty of the chamber plan can hardly exist by accident. Besides, due to the large distance between the monuments (400 km) it’s impossible, that the pattern simply has been copied. It was possible to ferret out a pattern, which was simply enough to be remembered. With it, after time went by and in remote places, every time again the same ground plan could be obtained. It starts off with the fact, that the oblique treshold can be created by a diagonal in a double square. Here the proportion 1:2 leads to an angle of 117º - the same as the angle between the long axis and the treshold. This diagonal is drawn three times (in a loop), after which an inscribed right angled triangle evolves with the ratio 3:4:5 between its sides (for a proof see the page Geometry in ancient times). Finally the top of this triangle is clamped by a parallel line to that of its base. This figure determines the plan of the chamber (light red in the figure).
Except for the construction with diagonals in the proportion 1:2, it’s possible to get a 3:4:5-triangle with diagonals in the proportion 1:3. This method we find with the hunebedden D25 and D26. Those hunebedden have far more stones than generally used for enlarged dolmens. By looking at the eastern half only, one gets a dolmen-like situation yet. In D25 this approach is supported by a difference in breadth of 30 cm between the eastern and western half of the hunebed. Moreover, some orientation lines on both sides diverse a little (respectively 143° and 140°). On the page Hunebedden with satelites an explanation is given for it.
As a result of Heggie’s first demand (see the page Accounts) we must ask ourselves, if Neolithic man was able to use such a pattern. Did the setup of a grid belong to their tool box? In one of the earliest treatise on mathematics, the Sulba Sutra (around 800 BC), the setup is presented as one of the standard constructions. Only a rope and a stick are needed. This type of writings form the remains of very old traditions. It cannot be said, how far back this tradition goes. But it could have emerged from the Neolithic Age very well. In the translation below, one gets a sqaure grid when also the ’diameters’ are involved to it.
When desiring a square, one needs to take a rope as long as a side of the square. Tie a knot at both ends and mark it at the middle. Setup an east-west line with it, having a pole fixed at its middle. Fasten both knots to the pole and draw a circle with the mark. Stick a pole at both ends of the diameter [= intersection of the circle with the east-west line]. Having one knot tied to the eastern pole, draw a circle with the other knot. Draw a similar circle using the western pole. The second diameter [= the north-south line] is obtained from the intersections of both circles. Stick a pole at both ends of the diameter [= intersection with the first circle]. Fasten both knots to the eastern pole and draw a circle with the mark. Do the same at the southern, the western and the northern pole. The intersections of the four circles produce the square.
Of course there are more ways to get the chamber pattern. For example by means of a stretchers rope,
which is known from ancient cultures (figure on the right) [6.13].
Step two (green) is executed when first a diagonal is drawn via the proportion
1:2 or 1:3 (blue and orange). For three reasons the construction in a grid is hold forth on this website:
(1) With the dolmens the grid has its own orientation.
(2) Repeatedly other chamber qualities then the orientation can be explained by the grid (e.g. the position of the gate).
(3) The construction via the grid can be seen as a starting point of a continuous development up to the earliest writings on math (see the page Geometry in ancient times.
For a matter of fact, it is conceivable very well, that more techniques have been used beside one another. The stretchers rope can be serviceable to setup the ’mirroring along south’, an important theme of the orientation grid. Using the rope one constructs a base line on a required azimuth and then creates the grid as in the Sulba Sutra.
The concept of mirroring around south needs an explanation. Arbitrary which azimuth has a counterpart, which mirrors around south. Here it handles about a special case of mirroring. A grid is placed on the norht-south line in such a way, that two orientation lines originate from it, which mirror around south. Often this grid isn’t the orientation grid itself, but an initial grid. Subsequently the diagonals in this grid determine the azimuth of the orientation grid. After constructing the mentioned pattern in the grid, an inscribed 3:4:5-triangle is formed, filling the chamber of the hunebed or dolmen. In the following illustrations the initial grid with the diagonals is placed at left and the working out with the hunebedden or dolmens at right.
Via the diagonals of the initial grid, orientation grids on 40° (blue) and 167° (green) are obtained. As well with Frauenmark 632 as with Barkvieren 92 only the orientation grid at 167° is in use. The mirroring around south reveals itself by respectively a diagonal and an end stone. In Frauenmark 632 the 40° orientation shows up as the orientation of the northern side stone. It disturbs the rectangular shape of the chamber, which is ’rectified’ again by a marking on the end stone. At first glance Barkvieren 92 seems to have an orientation grid at 40°, but this is not the case. The base of the inscribed triangle diverges 3° from the involved chamber wall and also the top is not positioned well (the red circles in the figure above). An orientation grid at 43° appears to be the right one. It is explained in the next section.
Serrahn 540 is not based on an initial grid. Its orientation grid itself is setup by mirroring around south. The mirroring becomes visible by the orientation of a side wall and a diagonal.
One can derive a 133° orientation (= 90° + 43°) directly from a grid at 167° via the proportion 2:3. In Barkvieren 92 the 167° grid is turned around the blue spot in the figure above *). As the eastern end stone at 193° fits in the 167° grid via the proportion 1:2, the western end stone at 16° fits in the 133° grid. Therefore the eastern and soutern and the western and northern walls stand at a right angle to each other, but yet they don’t form a rectangular chamber. In Frauenmark 632 the end stone stands at an orientation of 133°. The position of this stone is fixed in the grid via the proportion 2:3.
We also find an end stone at 133° with Bronneger D22. Here the orientation grid stands at 133° and the 167° orientation lines are derived from it. Nevertheless, taken theoretically, in D22 there exists a non measurable deviation of 0.4° in the orientation lines. On the page Parallel orientation lines D21 appears to have received its grid from hunebed D21. Subsequently, on the page Alignments, it appears that perhaps the 167° orientation in D21 is the result of a re-orientation. Since an 196° orientation line is possible in D21, the initial grid with diagonals at 164° and 196° (see below) seems to have been in use at an earlier stage. Then the orientation grid must have had an orientation of ½ atan(2:3) + atan(1:2) + 90° = 133.4°. When added to it a rotation with the proportion 2:3, this results in 133.4° + atan(2:3) = 167.1° for the orientation line. Reasoned from a mirroring around south with the proportion 1:2, we find this orientation line at 180° - ½ atan(1:2) = 166.7° instead. With the re-orientaton they haven’t been conscious of this small fault probably.
*) The orientation grid at 43° can be constructed in two ways, which differ from each other barely (see the frame above). Because of the symmetrical design of the chamber of Barkvieren 92, it seems implausible, that divergent orientation schemes have been used entangled. Therefore here is chosen for an derivation from the 167° orientation grid.
The initial grid has diagonals at 43° (blue) and 170° (green). G5 near Heveskesklooster uses the 170° as direction for the orientation grid. One of its diagonals runs along an orientation line. With Bronneger D22 the orientation grid lies at 43° and can be used in two ways. The concerning grids lie shifted half a position according to each other. (One could say also, that the grid should be more close-meshed.) In one position one of the diagonals of the dolmens runs along a grid line at 43°. In the other it’s the eastern end stone (S2), that stands with its flat outer side along a grid line at 133° (see the remarks in the frame above also).
Serrahn 541 is a special case. The comparison to hunebed D22 near Bronneger has lead to the assumption, that orientation grids are usefull to understand the shape of the ground plans. The orientation grids at 95° (blue) and at 148° (green) exist twice in the dolmen. The diagonals of the dolmen have the same orientation as the diagonals of the initial grid. Each runs along a grid line of the concerning orientation grid. The eastern side wall and the dividing stones in the middle stand at 212° and fit in the grid at 148°, so that the mirroring around south also is made clear in the plan of the dolmen.
The orientation grid of D26 can be interrelated with a secondary mirroring around south: the combination of azimuth 167° and 193°, as introduced above. The 193° orientation line runs free through the gaps between the side stones, but the 167° line reveals itself with a 1:3 proportion in the orientation grid only. Both mirrorings around south can be rendered into each other exactly: ½ atan( 2:1) = ½ atan( 1:2) - atan ( 1:3). Since people took a small fault for granted with the fixed relationship between 167° and 133° (see above), one may doubt if they were concious about the exactness now. On the other hand, one can give a proof, which allies to the pattern in the orientation grid:
The proof comes in two steps:
(I) the angle between the yellow arrows is made via the proportion 1:2 (’is an 1:2 angle’) and
(II) the yellow arrows mirror each other around south.
In both left figures the bold non-dotted lines make the same angle. Together those lines form the isoceles right angled triangle of the third figure from the left. Herewith it’s proofed, that the angles at the base of this triangle are the same (45°) - for us ’obviously’, in the Neolithic Age possibly not. In the third figure such a base angle appears to consist of a 1:2 angle (green) and a 1:3 angle (blue). The same isoceles right angled triangle occurs in the orientation grid (right figure, light red triangle), so that the angle of the yellow arrows must be an 1:2 angle (base angle minus an 1:3 angle).
The angle between the 212° and the 193° arrow must be an 1:3 angle (base angle minus an 1:2 angle). The angle between the 148° and the 167° arrow is an 1:3 angle too. The 212° and the 148° arrows mirror around south and the angles between the 212° and the 193° and between the 148° and the 167° arrows have the same value. From this results, that also the 193° and the 167° arrows must mirror around south.
In Emmen D39 the orientation of the initial grid matches the orientation of the hunebed. One of the diagonals of the chamber and the initial grid runs north-south exactly. With D40 it is the south-western side stone (Z1), of which the flat outer sides fit within the initial grid. Here it’s the north-western side stone (Z2), that at its chamber side runs north-south exactly. Neither with D39 nor with D40 an orientation grid at 0° is used, but at the other diagononal of the initial grid (53°) it does. The orientation lines in this grid appear to diverge 3°. This counts for a diagonal in D39 at 50°, for the outer side of the nothern end stone in D40 (S2) - also at 50° - and for a diagonal in D40 at 140°. On the page Hunebedden with satelites an explanation is given for the difference.
Generally the French dolmens south of the Central Massif are surrounded by a mound of small boulders - a less solid construction. Many stones are subsided (own observation in the Gard). One can see this for example on the ground plan of dolmen Bougon F. No restoration history is known from the dolmens displayed here. Nevertheless, with some restraint, an attempt is made to apply an orientation grid to them.
The grid with the proportion 1:3 is used as initial grid, of which the 162° diagonal fixes the direction of the orientation grid. The grid at 45° with the diagonal proportion 1:2 is used as orientation grid itself. Both grids result in identical orientations at: 180 - atan(1:3) = 135 + atan(1:2). As with the earlier discussed dolmens and hunebedden, the long side of the inscribed 3:4:5-triangle in D25 runs along one of the side walls. With the displayed French dolmens it runs diagonal through the chamber. This agrees with the observation of Chevalier, that the dolmens of the Langedoc type have a ratio of 3:4 between the side walls [6.14]. The dolmen Gouziac S has a different setup.
On this page only those ground plans are mentioned, that agree with the pattern. This may not give the impression, that the pattern can be found in all of the ground plans. The proportions are more or less like this: In almost all of the cases one can find lines, which occur in one of the orientation grids above. With a quarter of those cases due to the grid a situation emerges, that must be called implausible because of the other lines. With half of the cases the grid seems to determine the orientation indeed, but here the pattern doesn’t fall along the longitudinal orientation of the hunebed or dolmen. The remaining quarter exists of the mentioned ground plans above.
When no pattern is found, this doesn’t mean that it’s impossible to find one anyhow. Maybe with some hunebedden or dolmens there has been too little investment to find the pattern. By being applied to the obvious patterns it was possible to recover the pattern from ground plans, that were neglected in the first place. The priority lies with grasping the existing patterns and not with finding more.
Although all of the ground plans on this page are described from a steady approach using an orientation grid and often an initial grid, it appears, that only two of the fifteen cases come up with the same general orientation:
It’s clear, that one cannot speak of a uniform usage of the orientation grid. This page started off with a more or less similarity in the ground plans of some chambers, but this seems to be a by-product rather then the aim of the construction. Neither it can have been the intention to provide the chamber or its gate with a sudden orientation. In such a case people would have needed a few strategies only and what is more, the orientations itself vary to much for it. Maybe the orientation grid was employed to construct the inscribed 3:4:5-triangle, but then it surprises, that those triangles lie outside some chambers in part. The current data is too brief to draw conclusions on this point.
Although the above offers a lack of understanding of the mode of thought of the megalith builders, it does clarify the spread in the orientation of Neolithic burial chambers. The spread doesn’t need to be demystified by the rise of sun or moon, as the explorations of van Giffen and Langbroek suggest. Those explanations exhibit shortcomings with the too far nothern or southern orientations (see the page Former Duch research). Legion orientations can be setup via the variable usage of the orientation grid. Maybe the usage of orientation grids leads to some clustering of orientations. But, when the orientations of the six Dutch monuments in the list (27°, 58°/77°, 70°, 90°, 143° and 170°) are compared to the clusters in the data of González-García en Costa-Ferrer [6.15], then only one orientation (70°) appears to be part of a cluster. So the statistical approach doesn’t seem to be the appropriate means to put the usage of orientation grids to the test. For the time being nothing else is left, then to investigate each hunebed or dolmen separately - a time-consuming task.
A final remark on the mirroring around south.
The determination of due south can be called an amazing achievement of the Neolithic Age.
Although realised by simple means, it requires the insight, that one needs to work either perpendicularly or levelly.
Next options are modern fantasies on how people could have accomplished the task:
(1) One can clamp the path of a star around the celestial pole between two plummets. Due north lies exactly in the middle. This should be applied during wintertime at best, since then the nights are long. Otherwise the star reaches one extremity at night and the other during daytime.
(2) With a levelled stick one can create an artificial horizon. Due north or south lies exactly between the ’rising’ and ’setting’ of a celistial body.
(3) One can follow the shadow of a pole on an exact vertical surface. By means of a plummet the lowest point is found. From there to the pole makes due south.
The Sulba Sutra passes on a very clever solution. Most of the time its geometric constructions start of by stretching a rope east-west. This is how they managed:
(4) One puts a pole perpendicularly on levelled ground and draws a circle around it with a rope. Then one marks the positions where the shadow of its top hits the circle - one for the rising sun and one for the setting sun. Stretching a rope between those points delivers true east-west. Due south is obtained geometrically afterwards.