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> they say) ring of the Stones of Stenness; spaced for 12 megaliths with
Eureka, Dave, you have it, the hexagon inscribed within a circle! I even used this for something a while ago, so can't see why I missed it here.
However, this came from the Greeks ~2000+ years ago, not Neolithic folk (NF) 5-6000 years ago, so it amounts to proposing that the NFs must have discovered the inscribed hexagon arrangement independently themselves. I don't think that even earnest contemplation of a regular hexagon like a bee's wax cell would suggest immediately to the observer that for a regular hexagon, radius R exactly equals side length L as a neat rule. On the other hand, if some enterprising NFs had a radius rope and two pins like you suggested and stepped around the perimeter of their initial circle accurately, at the 6th step they would have found themselves exactly back at the origin, so could plausibly have discovered the R=L rule that way and then passed it around by word of mouth to others. Could this even have filtered down to the Greeks?
Steve
________________________________________
From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca] on behalf of David & Alison Webster [dwebster@glinx.com]
Sent: Monday, August 18, 2014 2:03 PM
To: naturens@chebucto.ns.ca
Subject: Re: [NatureNS] Neolithic stone rings etd.
Hi Steve, Jane & All,
The logical way to lay out a 12 post observatory is as follows.
1) Find a relatively level area of open land with unobstructed horizons from ~NE through S to ~NW.
2) Prepare 7 relativey slim and untapered, smooth rossed posts; say 2" in diameter
3) Select the center point and mark it with one of these posts.
4) Select a radius for the circle, braid a loop in one end of the rawhide length that is large enough to just slip down over the posts as this will be used numerous times. A wooden yoke at the other end would increase precision.
5) Sight from the center post to the Pole Star and mark the position of the North and then the South posts using the radius strand. These act as a baseline and enable checking the length of the rawhide radius strand which if not well oiled and protected can shrink or stretch.
DIGRESSION:
The hexagon must have been noticed even before the first crude tools were made; Bee & wasp hives/nests, snowflakes, drying silty mud deposits, Thallose Liverworts, some large celled Mosses... And if the 6 points of a hexagon are joined by drawing lines between opposite points you have a cluster of six equilateral triangles. Therefore the radius of a circle is exactly equal to the distance between the six points of a hexagon that fall on that circle.
END OF DIGRESSION
6) Using the above one can proceed to fix the location of the remaining 4 points of the hexagon. If the ground is readily marked (weak sod or cultivated) one could simply inscribe an arc from the center post at the approximate location of the next post and then measure this exactly by moving the radius strand to the previously fixed post (initially the North or South post). If the ground is not readily marked then use of two strands of equal length would be indicated.
7) If one proceeded to locate post positions, starting at the North post, then the distance from the 4th post should be one radius strand from the South post provided no errors have been made.
8) Having installed the 6 posts of a hexagon one need only bisect the arc between adjacent posts (as before, most readily done if the soil is easily inscribed); bisect the line between posts, mark with temporary post flush with ground then swing the radius strand around the center post until it lies over the flush post. Repeat five more times and you have 12 posts equally spaced around a circle.
After this has been digested I will describe how to mark a 60 post circle. Some decades ago, for amusement, I went back in time mentally and worked out a way to divide a disk edge into 360 equal parts using stone-age hardware and the 60 post layout would use the same stone-age "math".
Yt, Dave Webster, Kentville
----- Original Message -----
From: "Stephen Shaw" <srshaw@Dal.Ca<mailto:srshaw@Dal.Ca>>
To: <naturens@chebucto.ns.ca<mailto:naturens@chebucto.ns.ca>>
Sent: Monday, August 18, 2014 2:25 AM
Subject: RE: [NatureNS] Neolithic stone rings etd.
> Hi Dave: You need an astronomer with an interest in history for this, so stand by, hopefully, for input.
>
> Meanwhile, this astronomical observatory idea originated I think with Alexander Thom, based on his idea of a a common unit of length, the megalithic yard (MY) of 2.72 feet. This unit supposedly had been used with precision to lay out British and French neolithic stone circles. While this seems not to have been entirely discredited, later critics doubted that there was a unit with this precision in universal use, and that distances could have been measured adequately instead simply by pacing-out, not necessarily by using a common physical yard-stick. I can't remember the connection, but the MY supposedly was somehow related to an astronomical cycle, indicating that you must have had active neolithic astronomers to make the connection. Perhaps someone else can remember the connection, or if I've got this wrong.
>
> Not sure about the universal '12' ideas. The main units of time that we and presumably earlier populations used were based on 3 quite different astronomical cycles that are unrelated. Days are/were measured based on Earth's daily rotation on its axis, easily counted though not precisely constant. Months depended on the Moon's rotation about Earth, easily observed as recurring phases of the Moon. Years are/were measured in time units based on the Earth's orbiting around the Sun -- much more difficult to calibrate accurately, probably accounting for the need to calibrate by building fancy sunrise-observing structures, accurate to the day at solstices. Very important for correct crop planting. Unsurprisingly, neither of the smaller units in use at present divide exactly into the largest unit, the year, or into each other, hence yearly movement of Easter, calendar day regression and the need for leap years. Not clear how you would use a megalith with one annually precise alignment axis to tell the time (for instance the day, month) at other times of the year.
>
> I've forgotten most Euclid, but how do you subdivide a circle easily ('a snap') into 12 subunits? I can see how you draw the first line and find its centre (will become the centre of the circle) with a rawhide compass-divider, and how you can draw the second diameter at right angles to this with the same gear, and then complete the circle. You are then left with a circle with 4 equal quadrants, each of which has to be subdivided finally into 3 segments to make a total of 12, like the