The relationship of the radius or diameter of a circle to the size of its circumference is governed by the irrational constant Pi = 3.1415... where the fractional part is endless. This means that, in theory, using a given number of length units to form the radius R will mean that the circumference (2 times Pi times R) cannot be made up of a whole number of the same units. Ancient metrology solved this and other problems by developing a whole range of interrelated units of length - a concept alien to our selves where our unit of length is usually just the metre or the English foot.
In other words, by having a range of units related to one another, a type of calculation was possible that today we would achieve using trigonometry and other techniques based upon the notational mathematics we now use. This makes ancient metrology a candidate for the prehistoric mathematics that is implied by megalithic monuments.
A number of rational approximations to Pi existed in the ancient world but the simplest accurate one is 22/7. which means that a diameter of a circle seven units in length will produce a circumference 22 units long. However, to be really useful, a metrology needs to be able to divide up a circle into any number as required, just as we do when we divide a circle into 360 parts and call the angle from the centre of each, one degree. If we can place 360 around a circle then a degree scale can be produced and how are degree scales made anyway?
Ancient metrology decided on a single unit and called this unit one - a fact revealed conclusively by John Neal in his All Done With Mirrors. Having worked for many years with this fact it continues to reveal the hidden nature of metrological buildings from the Megalithic to the Gothic period.
To build the system, the unit one is then extended or contracted into new units of measure that are a rational fraction of a foot, the English foot (as we call it today). Thus a Sumerian foot in its simplest form is 12/11 feet and this unit can be found in the vertical dimension of the Great Pyramid.
If we imagine one Sumerian foot as a radius, then the circumference will be 12/11 times 4*11/7 feet long and the elevens will cancel to leave 4*12/7 or what we would call four Royal cubits, again in their basic or root form - the unit of length most associated with the Egyptian builders. It is as if Pi has been transformed into 4 rather than being 3 plus something.
Matrix Diagram of mentioned Units of length
in their relationship to one another
Four Royal cubits might be called a megalithic rod of 2.5 megalithic yards by Alexander Thom and the common unit for the cubit and the megalithic yard is a 10 digit Palm, which is a tenth of a rod. All of this rich cyclicity within metrology was a functional idiom learnt by its practitioners.
The upshot is that one can build a radius with a required number of Sumerian feet in the radius and see that linear dimension translated into the same number of Royal rods on the circumference. A radius of 360 Sumerian feet would generate a degree circle in which an observer could see degrees on the radius as markers spaced one Royal rod apart.
One way in which metrology could calibrate a circumference
with 360 equal units of length
The choice of 360 for degrees comes from its similarity to the number of days in a year and its capacity to factor purely canonical numbers, the primes 2, 3 and 5. It is 5 less than the number of whole days in a year and 6 less than the whole number of earthly rotations in a year. 360 divides by 72 five times and 365 divides by 73 five times whilst 360 divides by 60 six times and 366 divides by 61 six times. The former gives us the Venus calendar with 73 day units and the latter gives us the Saturnian calendar with 61 day units whilst 360, the "common denominator", gives us convenience in aggregating degrees into 30, 12, 10 and so on yet gave many cultures a calendar with five extra days, the "Neters" in Egypt.
Calendars and degrees are therefore related and one use for placing a known number of divisions upon a circumference is to make that number resemble the days in a year, month, lunar orbit or whatever, since then you can enact the year as the re-entrant species it is, for every cycle is a snake that eats its own tail, every end is a new beginning - not just in self-development books but also in the sky!
Without ancient metrology this whole procedure is obscure and lack of metrological knowledge is holding back our cultural perception of what was possible and sophisticated in the techniques of the monument makers. Nothing can reveal what a pyramid or stone circle was doing without ancient metrology but the whole subject is locked out of official science and general knowledge for various reasons.