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>> You don't need to be a Greek Philoso
Content preview: Hi, I teach this same process in grade seven math! We use
a primitive compass, a paper clip and two pencils. We also look at the use
of this symbol in historic terms, a hex. The students all associate "hex"
with a bad spell used by a witch or sorcerer, but soon find that it was used
in northern European history as sign or symbol of good luck and fortune.
The Pennsylvania "Dutch" use it as a protection on their barns, as a bearer
of protection. [...]
Content analysis details: (-1.9 points, 5.0 required)
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-1.9 BAYES_00 BODY: Bayes spam probability is 0 to 1%
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Hi,
I teach this same process in grade seven math! We use a primitive
compass, a paper clip and two pencils. We also look at the use of this
symbol in historic terms, a hex. The students all associate "hex" with
a bad spell used by a witch or sorcerer, but soon find that it was
used in northern European history as sign or symbol of good luck and
fortune. The Pennsylvania "Dutch" use it as a protection on their
barns, as a bearer of protection.
Interesting wondering how so many discoveries could have been made by
"primitive" people without the computers and communication of our world.
Cheers, George Forsyth
Quoting David & Alison Webster <dwebster@glinx.com>:
> Hi Steve & All,
> We appear to be in essential agreement on this. Practical
> geometric insights would likely all have come by accident in the
> course of small scale and perhaps perishable decorative art
> exercises; and once recognized and learned perhaps incorporated as a
> part of practical culture long before any attempt theoretical
> analysis. The latter requires leisure.
>
> That same article provides a good example of this process on page
> 33. where parallel evenly spaced straight lines engraved in stone
> cross a sequence of other straight lines to produce a double row of,
> what we would call isosceles triangles. And then secondary patterns
> are inscribed within these triangles; some messy and some
> attractive. The two long sides of one of these original triangles is
> neatly bisected and the points joined to form a triangle of
> identical shape but half as high. Then the base of the original
> triangle is bisected and the points joined to form a total of four
> identical triangles all within the original triangle that was twice
> as high.
> If that rather attractive pattern were to become widely used
> then someone would eventually notice that when the height of a
> figure like this is doubled the area will be four times as great.
> And if this became understood then someone might notice that the
> same applies to squares and rectangles. And those experienced in
> dividing fields for various purposes would say "Well duh".
> Decorative arts would also likely have revealed the circle
> hexagon connection. If drawing careful circles using a forked stick
> with one side sharpened and the other charred
> had come into common usage at some point then someone would
> eventually have noticed that by placing the pointed arm anywhere on
> a circle the charred end would pass through the center. And someone
> would have noticed that this can be repeated 5 more times to yield
> an attractive flower-like pattern with six-fold symmetry. Drop the
> arcs that extend beyond the original circle, join the adjacent
> points of the 6 petals and you have a hexagon just fitting a circle.
> Perhaps more than one person on naturens will recall attempting
> to draw this figure exactly, using an even more primitive compass,
> as a pre-school rainy-day amusement.
>
> Yours truly, Dave Webster, Kentville
>
>
> ----- Original Message ----- From: "Stephen Shaw" <srshaw@Dal.Ca>
> To: <naturens@chebucto.ns.ca>
> Sent: Friday, August 22, 2014 3:48 PM
> Subject: RE: [NatureNS] Neolithic stone rings - encore.
>
>
>> Hi Eleanor,
>> Many years ago I recall reading that the neolithic denizens of
>> Skara Brae used to cache the bones of their forebears in an
>> ossuary, on stone ledges somewhere in their dwellings. One of the
>> memorable findings was that experts analyzed these bones as to time
>> of death, revealing that practically nobody at Skara Brae had lived
>> beyond the age of 30, apparently testifying to the hard life there.
>> I couldn't find any mention of this latterly, searching a couple
>> of recent sources e.g. Wikipedia. Did you come across any such
>> information when you were there: is it still believed that they had
>> nearly all died by an age that we would consider a very young? I'm
>> not sure that this is reflected in other early societies -- not the
>> contemporary Egyptians, I think, who however were presumably much
>> better fed.
>>
>> Hi Dave: Maybe this flogging a dead horse, but I think you have it
>> backwards. In fact I suggested that the neolithic farmers could
>> well have 'solved' what would later be called the "inscribed
>> regular hexagon conjecture" by a simple practical-knowledge
>> construction procedure of the sort that you advocate, without any
>> foundation in theoretical geometry that would not arrive until much
>> later, usually associated with the Greeks. At the same time, it's
>> not clear why stone circle-makers would have been sequentially
>> pegging out the boundary of a large circle by trial and error to
>> make any such discovery (if that's how they did it), if they didn't
>> have some informal geometrical insight in the first place. But I
>> doubt that they could get that simply from looking at snowflakes,
>> without a magnifying glass and ruler, though we did see plenty of
>> snowflakes when we lived in Scotland.
>> Steve
>> ________________________________________
>> From: naturens-owner@chebucto.ns.ca [naturens-owner@chebucto.ns.ca]
>> on behalf of Eleanor Lindsay [kelindsay135@gmail.com]
>> Sent: Tuesday, August 19, 2014 11:45 AM
>> To: naturens@chebucto.ns.ca
>> Subject: Re: [NatureNS] Neolithic stone rings etd.
>>
>> On a completely different aspect of this topic, I spent time in Orkney
>> in the '70s during the early displays of the first discovery of ancient
>> dwellings which became exposed at Skara Brae after a major storm tore
>> masses of turf off the nearby shoreline, uncovering an entire
>> prehistoric village of stone houses with connecte