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Thanks. In laymans's language, what is the simplest argument to refute the coincidences that are shown?

 

 

 

There's no apparent evidence that it ever was built as a complete a circle: The section to the South West (at the back of the Great Trilithon) is generally assumed to have existed. It is a good logical assumption though:

 

http://en.wikipedia....:Stone_Plan.jpg

But there is evidence that the sarsen Circle was complete, here it is: http://www.solvingstonehenge.co.uk/page7.html

If you mean Pytheas of Massalia's trip, it was much much later, around 325 BC.

 

 

 

Where do the gold come from? are there gold mines around?

OK there was gold to be found in Wales, Devon, and Ireland, as for the tin used in early Bronze Age artefacts: Cornwall, Copper too (Also from North Wales)

I just tend to be sceptical about the general expectation that ancient peoples were much more advanced than we have assumed. At one time people were amazed to find that many lengths of buildings made by the Ancient Eqyptians were multiples of pi, thus indicating that they had discovered this mathematically sophisticated value before the Ancient Greeks. It was later discovered that the Egyptians measured large distances over land by using a cycle on a pole and counting the number of cycles, thus making distances a mulitiple of pi, even without the Egypticans knowing the number.

The point is that the recent research shows that the 'math’s' at Stonehenge was not advanced, it was however the principle behind its design, They simply used rope and peg surveying, e.g. they could lay out an accurate circles, squares, hexagons and octagons (consider the Stonehenge Station Stones, the two surviving stones, and the pits for the missing pair – they are set on the vertices of two opposing facets of an octagon). Also when you look at near contemporary early Bronze Age artefacts, such as the 'Bush Barrow' and 'Clandon Barrow' lozenges, it’s self evident that these prehistoric communities had a sound working knowledge of geometry; nothing 'advanced or sophisticated, just empirical, but given the date for western Europe simply remarkable.

You make some very good- and interesting points. Anyone who really want to know what communities contemporary with Stonehenge knew about geometry could look at the 'Bush Barrow Lozenge', a remarkable gold sheet decorated with motifs derived from circles and hexagons. There was also a smaller lozenge shaped artefact from the same burial site that was based on an hexagon, and from a burial mound at Clandon (Dorset, England) a similar geometric artefact was based on a decagon; these objects are almost 4,000 years old.

I wanted to put a link about "empirism" but the word (empiricism) has a different meaning in the english language.

Practical skill, yes, knowledge from experience: a great force we are losing bit by bit.

Any profession has its little mysteries, owned only by the professionals. Old professions have dissapeared, skills disappeared.

How to scarve a rock without a jackhammer, or moving a 20 tons object without a crane, that seems inconceavable. But they did. Not by calculating, but through practical knowledge.

 

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I remember some years ago at a work of restauration of a neoclassical building, a worker standing sceptical in front of a little problem: the first step of the outer staircase to the building had moved down from its place about 10 cm. It was a solid block of pentelic marble about 3 metres long, 20 cm height, 40 cm depth. estimated weight about half a ton (500kgs). He told me not to worry about. I went on my inspection and after half an hour came back to see what to do. The problem was already solved. The man all alone had lifted the marble block and put it back, just like that. With a lever I guess, he wouldn't tell me, only smiling.

 

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Some other fabulous artisan, almost illetrate. He sells and cut marbles.

One day at the office, explaining how he solved one of his problems.

He is paid following the square meters of delivered products. When the product is rectangular, all well. When it has a peculiar polygonal scheme, that is still o.k., he knows the formula for a triangle (basis by heigth divided by 2). But when you cut a circle, how to calculate the surface?

His thought (I hope it was a true story):

"When I cut a circle, I can put a rope all around and get very easily its perimeter"

"then I thought with my practicle mind, that each line coming from the center and going to the perimeter (the radius) is a very tiny tiny triangle, and that there are as many such triangles as the perimeter is long. And then, if I get the surface of all these tiny-tiny triangles I get the surface of the circle".

 

Which is very correctly perimeter by heigth divided by 2 or [math](2{Pi}R)R/2[/math] = [math]{Pi}R^2[/math]

 

(trouble with Pi in LaTeX)

Architects and Engineers did not build Stonehenge just like Donald Trump did not build Trump Tower . Stonehenge was built by slaves ( IMO ) .

Slaves could have not possibly have built Stonehenge without any technical input, and Donald Trump or even Donald Duck could never have built Trump Tower without a design team! Ancient Egypt had its own class of architects and surveyors, it’s documented, we just don't have written records for Stonehenge. I have to stress that those stones (weighing up to 50 tons) are set accurately to just a few centimeters so that their inner faces formed an accurate circle; and the tops of the lintels were near perfectly level. I honestly would expect more appreciation and thought from a math’s forum!

I'll hazard to state that , I could draw a few circles and lines to intersect in simple ways and before I know it , there would be a lot of Euclidian geometry theorems applicable to the situation .

 

The converse of this statement which I would ask about , is , if I apply a lot of Euclidean geometry theorems to this situation , will I just finish with a few circles and lines that intersect in simple ways and thus , that is the way that they were originally selected 5000 years ago , nothing complicated , just simple ? .

 

 

 

 

That’s exactly the point, it IS simple, no complicated sight lines or astronomical calculations, just simple geometry.

Just like any other construction the Neolithic architects and engineers who built Stonehenge knew exactly what they wanted long before the foundations were dug. The stones were positioned in respect of a vision of their vision - a superb premeditated geometric structure. It was also largely prefabricated, just look for example at the complex jointing in the lintels, they can only have been created off-site and must have been trial fitted on the ground (which also indicates just how much thought and planning went into the design). As for all the so called alignments, it has only one, an axis of symmetry; that of the midwinter sunset and midsummer sunrise. Now where does this leave Stonehenge studies? Well exactly where it belongs, as investigation into the mindset behind its construction, a mathematical and geometric problem as much as an archaeological or ‘astronomical’ one.

In a recent publication ‘Solving Stonehenge’ it is revealed how every stone conforms to a precise mirrored symmetrical plan, and that markers must have been placed in exact positions against which the centre inner faces of the uprights were set. We are talking of course about the iconic sandstone (sarsen) monument, but there is evidence that geometry played a role in every phase of construction from around 3000 BC to c. 1600 BC. Mathematicians should now become involved in exploring the potential significance of the geometric arrangement, especially that of the central ‘horseshoe array’ formed by the trilithons. The prehistoric surveyors used ropes and pegs, for which we can read ‘straightedge and compass. We start with a sight line, towards the midwinter sunset, then a circle, then a triacontagon (beginning with a hexagon) against the vertices of which the exact centre of the inner faces of the circle stones were positioned (and by default the joints of the lintels). From these same 30 vertices the locations of inner faces of the 10 Trilithon upright were established; all that is with the exception of the two uprights of the Great (midwinter) Trilithon; the better faces of which look outwards towards the winter solstice sunset. Come on guys what is the significance of how the Trilithons were arranged, and why certain vertices were chosen, is there a numeric sequence to be found?……

An image showing the method seemingly used by the prehistoric to set out the trilithons can be found here: http://www.solvingstonehenge.co.uk/trilithon_geom2.html from that you can work out the rest.