Landforms are past (or present) interpretations within a landscape which enable the land to represent meanings found within astronomical time or ideas about the ordering within any centre and its environs. There is evidence for the widespread use of landforms in prehistoric and ancient cultures.

Einar Palsson [1] saw the myths of foundation for Iceland's settlement (in 930) had Pythagorean roots. This manifested as a geometric connection between places on the landscape, especially on the south western region near Reykjavik, its only city. Coherence was established through organising space according to centres (things), circles and their diameters, the circles punctuated with places and alignments to other places, horizon events or cardinal directions.

Palsson figure 2 540

Figure 1 The Cosmos of Rangarhverfi

In 1972 John Michell first inferred an enormous ten-sided form nearly sixty three miles across, in which important historical and neolithic sites had been intended as ten vertices around an ancient centre, signified by a Whiteleafed Oak (see previous article extract). 

DecagonCentres nocircles 

Figure 1 The Decagon of Perpetual Choirs, anchored upon Stonehenge, the Solstice sunrise in summer and set in winter

17 July 2017

The fields of ancient Greece were organised in a familiar way: strips of land in which a plough could prepare land for arable planting. Known in various languages as furlong, runrig, Fr. journel, G. machen etc, and in Greece there was a nominal length for arable strips which came to be associated with the metrological unit of 600 feet called a stadia. The length of foot used was systematically varied from the foot we use today, using highly disciplined variations (called modules); each module a numeric ratio of the Greek module, whose root foot was the English foot [Neal, 2000]. These modules are found employed throughout the ancient world, lengthening or reducing lengths such as the stadia, to suit geometrical problems; such as the division of land into fields (figure 1). The English furlong is a stadia of the Saxon module whose root value is 1.1 feet, hence it is 660 feet long and remains one eighth of the English mile (5280 feet), the mile being defined in ancient metrology as 5000 feet.

Anthropic Farm Units Oxgang

Figure 1 The land area of an acre x 15 considered the amount of land tillable by one ox in a ploughing season

The Distribution of Land

The word stadia became implicit in our sports stadiums because ancient Greeks used field areas as racetracks for their competitions. Their greatest games was held at Olympia’s racetrack, site of a pan-Hellenic Games now re-instituted (since1886) as today’s Olympic Games. Whilst the modern Olympics are competitions between states, racing was mythologically significant in ancient Greece. The original stadia were simply field-shaped runways; to an endpoint about a furlong (or "fur-rows long") away. Later two straight tracks were joined together by a two semi-circles (or sperium) allowing indefinite lengths of race, and giving us the modern type of stadium.


 Figure 2 The Racetrack at Olympia

This article explores another modern and highly transient manifestation belonging to the category of Landforms, the crop circle. Thought in seventeenth century England to be the work of a mowing devil, and more recently hoaxers, the large crop fields created since the post-war tractor revolution play host to "sacred art" designs that farmers find intrusive, attracting members of the public (to be a-mazed) and aviators to curate these patterns for posterity. The tabloids used to indulge full page colour sections to crop circles but then were dissuaded perhaps by officialdom (we are mad) and apathy (we lose interest) since the finest examples do not give any trace of manual construction.


Figure 1 The first known newspaper story involving a Crop Circle

The majority of reports of crop circles have appeared since the late 1970s[12] as many circles began appearing throughout the English countryside. This phenomenon became widely known in the late 1980s, after the media started to report crop circles in Hampshire and Wiltshire. After Bower's and Chorley's 1991 statement that they were responsible for many of them, circles started appearing all over the world.[10] To date, approximately 10,000 crop circles have been reported internationally, from locations such as the former Soviet Union, the UK, Japan, the U.S., and Canada. Sceptics note a correlation between crop circles, recent media coverage, and the absence of fencing and/or anti-trespassing legislation.[30]  See <>

These days we take a measurement or define a length and call it a radius or diameter for a circle, using an irrational value for the ratio between a radius (or diameter) and the circle's perimeter, called PI - a Greek letter - which is 3.141592654 etc, where the fractional part has no limit of non-repeating cyclicity. 

Circumferences of Ancient Circles

In the ancient world, irrational numbers like PI required one to find an accurate rational approximation, in the form of a ratio between two whole numbers (called integers). The simplest and most accurate of these, rather than 3.141592654..., was 22/7 = 3.142857 , which meant that if a diameter was considered of seven parts then the circumference produced when arcing a rope around a central peg would be 22 of the same units. Since that rope from the centre would be half the diameter then if the diameter is 14 units, the rope is half that or seven units and the circumference must be twice 22 units long or 44 units. The advantage of seeing the diameter or radius as containing seven units is that the denominator of 22/7 divides into those seven units leaving the circumference as 22 or 44 units. 

Another habit of the ancient world was to analyse geometrical situations in terms of an underlying grid, so with a radius of seven units the following figure shows the situation "on the ground":

Grids 28 22. Perimeter

Figure 1 The Circle Radius seven for a PI of 22/7 leading to 44 units around the perimeter