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> 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
Hi Steve & All,
I think you are confusing theoretical logic with practical know how and
these northern folk had an impressive amount of know how.
For example, the walls of the Knop of Howar (occupied 3700 BC-1800 BC)
are still standing. How many of our structures will still be around 4000
years from now ? They lived on islands so likely knew how to build boats
that could actually be steered ( able to go out, turn around and come back)
and which cost less than a king's ransom.
You don't need to be a Greek Philosopher to notice that the 6 points of
an undamaged snowflake are of equal length, and would therefore fit a circle
of diameter equal to the distance between opposite points. And you need only
look at some of those prehistoric cave paintings or ornamented spear
throwers to realize how visually gifted some of these early people were.
Ivory and bone needles, some so thin that horsehair was the probable
thread, date from 15,000 BP. It takes skill and a steady hand to craft the
necessary stone gravers and then carve and polish even a relatively crude
needle.
Over much of the last 10,000 years fires were made using a fire drill or
a fire plow. Try this some fine afternoon, as a test of eye-hand
coordination and physical stamina.
Based on current conditions around the world and examples from recorded
history and prehistory that I have noticed, I suspect that, at least over
the last 30,000 years, there has never been a shortage of creative and
inventive people, only a shortage of conditions in which these qualities
could be exercised without penalty.
Yt, Dave Webster, Kentville
----- Original Message -----
From: "Stephen Shaw" <srshaw@Dal.Ca>
To: <naturens@chebucto.ns.ca>
Sent: Monday, August 18, 2014 3:30 PM
Subject: RE: [NatureNS] Neolithic stone rings etd.
> 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 histor