**Quote from article (Sarah Knapton, Telegraph Science Editor)**

*“One contributor, megalithic expert Robin Heath has even proposed that there exists a great Pythagorean triangle in the British landscape linking Stonehenge, the site from which the Preseli bluestones were cut in Wales, and Lundy Island, an important prehistoric site.”*

*Pythagoras’ discovery that the sum of the areas of two squares on the sides of a triangle will add up to the area of a square on hypotenuse has been used for millennia to help builders attain perfect right-angles.”*

How much longer do we have to put up with this attempt to portray our Neolithic forbears as sophisticated mathematicians, astronomers, cosmologists, all based on the arrangement and/or alignment of standing stones (for which there can be simpler more down-to-earth reasons as proposed earlier on this site)?

The idea that one needs Pythagoras (or pre-Pythagoras!) theorem merely to construct a right- angled triangle is fatuous in the extreme. All that’s needed is a stake and a line! (Apologies btw for the quality of this hastily-drawn diagram, showing 3 simple steps. labelled A, B and C …. The final triangle has sides in the correct Pythagoras ratios, e,g, 3, 4 and 5, as shown, but one does not, repeat NOT, need to know those proportions in advance!)

See also this article on the same idiotic claims penned by journalist Sean Martin in the Express (just spotted):

More to follow… Comments invited.

**Friday June 22**

Here’s an animated version of the simple technique used above, employing just a ruler and pair of geometry set compasses, courtesy of YouTube:

Note the official description of the procedure, which is not “constructing a right angle” but creating a “perpendicular bisector” to any given line. The introduction of the right angle is incidental, or a bonus if the right angle *per se* is the desired outcome.

One other thing: in my diagram I deliberately set out to create a 3,4,5 right-angle triangle (that being the simplest set of numbers that conform to the Pythagoras theorem: the square of the length on the vertical side plus that of the square of the the length on the adjacent side being equal to the square of the length of the hypotenuse.

**3 squared+ 4 squared = 5 squared (i.e. 9 + 16 = 25)**

I didn’t need to use the 3,4,5 proportions, needless to say. One has only to chose the desired length of one of the 3 sides of the desired right-angled triangle, then to choose any value for the second. The length of the third side is then predetermined by the Pythagoras relationship.

It would of course be possible to construct a right angled triangle, at least in theory, if one had three lengths of string or rigid material in the proportions 3,4 and 5. But that IS using a prior knowledge of Pythagoras theory, which I strongly doubt was the case where our Neolithic forbears were concerned. It’s far more likely they used the ‘perpendicular bisector’ method as demonstrated above, first by me on the dining room table, and shown more professionally step-by-step in the YouTube clip. Or maybe there’s an even simpler method that has not yet occurred to me (?).

Are there any natural right angles in Nature, not counting those blockheads who continue to dream up wild explanations for Stonehenge and other standing stones? 😉

Yes, there is another method of creating a right angle. It uses **Thales’ Theorem**, and starts by drawing a circle, adding a diameter, then using that diameter as the first side of a triangle with its vertex on the circle’s circumference. The angle at the circumference is always a right angle:

**Sunday June 24**

So why all the interest in triangles, right-angled ones especially? The Knapton article provides a brief clue. It’s given in this short passage: *(Apols, I’m repeating what’s appeared already at the start)*

“One contributor, megalithic expert Robin Heath has even proposed that there exists a great Pythagorean triangle in the British landscape linking Stonehenge, the site from which the Preseli bluestones were cut in Wales, and Lundy Island, an important prehistoric site.”

I’ll return later maybe to the tiny Lundy island, stuck out there in the Bristol Channel. “Important prehistoric site”? Really? See this link to the archaeology of Lundy, which is mainly focused on the Mesolithic era (pre-New Stone Age) and Bronze Age, with scarcely a mention of the Neolithic era.

*Late insert: from the web: *

*Mesolithic Period. Mesolithic Period, also called Middle Stone Age, ancient cultural stage that existed between the Paleolithic Period (Old Stone Age), with its chipped stone* *tools, and the Neolithic***Period** (*New Stone***Age**), **with its polished stone tools.**

I can think of a better geometrical explanation for Stonehenge being where it is, and yes, it does involve right angles, there being 4 to a RECTANGLE (forget those triangles and Pythagoras):

Here are two hastily constructed diagrams, obtained using the nearest atlas to hand of Britain (the southern half especially), now defaced on the inside front cover.:

Here’s a close up view of the point of intersection:

So what’s the significance of my rectangle? Can you guess, based on the central proposition of this site, namely that Stonehenge was designed to attract voracious coastal seagulls for the purposes of pre-cremation “sky burial” (aka excarnation) of the newly-deceased? Given the amount of work that went into creating the gull-friendly artificial “cliffs” (*and* cliff ‘ledges’) that we call Stonehenge by means of those massive crosspiece lintels, there could only be one Stonehenge to serve a large part of southern Britain, thus minimizing the distance that the bereaved needed to transport themselves and their deceased loved ones. That rectangle and its central point represents the happy medium: the bereaved walked the minimum *average* distance, while gulls flew the minimum *average* distance from as many points as possible on the southern English/Welsh coastlines (Bristol and English Channels especially).