#### Grids of Squares & Flattened Circles

There is a common approach in ancient building based upon the establishment of a grid of squares, as a framework for the geometrical construction of buildings, from stone circles to Egyptian and Greek temples, to Roman and Orthodox Basilicas, and to Gothic and Enlightenment buildings, plus in Indian temples. Just as one builds foundations, all that is inside a building is controlled by numerical ideas. I have therefore published some work I did to show how flattened circle, in megalithic times, could have used what came to be Egyptian methods for laying out building works and to not always depend on the ropes and stakes of the free style geometrical construction which led to analytical geometry, compass and straight edge.

#### Peat Fires revealing Rock Art

There have been a number of large peat moor fires in England and one of these in North Yorkshire revealed a few megalithic sites. I have republished my own interpretation of a significant pattern made on a major flat stone as part of an egg-shaped stone circle. The egg can be seen in the work of Alexander ThomScottish engineer 1894-1985. Discovered, through surveying, that Britain's megalithic circles expressed astronomy using exact measures, geometrical forms and, where possible, whole numbers. as based on the near-Pythagorean triangle with sides {17 17 **24.0416**}. When Thom’s plan is laid over that of the excavation (*Rock Art and Ritual *by Brian Smith and Alan Walker), one can see there is a close fit to the excavated site. When the egg is expanded to fit the line drawn by the excavators, the units of the geometry are 1/2 foot (6 inches) so that 17 = 102 inches (8.5 feet), 24 = 144 inches (12 feet) and 12 = 72 inches (6 feet), possible by overlaying different plans, one with the scale shown!

*Geometry of the stone egg where the rock art was found on one of its stones. Note the alignment of the egg’s axes to the cardinality of the sun’s solsticeThe extreme points of sunrise and sunset in the year. In midwinter the sun is to the south of the celestial equator (the reverse in the southern hemisphere) and in midsummer the sun is north of that equator, which is above the geographical Equator). extremes at that latitude.*

#### Chalk Drums to generate pi

When I joined the Prehistoric Society for a year, an article about megalithic chalk drums being found with strange decoration which may depict PIor π: The constant ratio of a circle's circumference to its diameter, approximately equal to 3.14159, in ancient times approximated by rational approximations such as 22/7., since their diameter allows rolling them to count out a given type of foot measure. This may be why some are not carved because they were heavily used while others could have been metrological standards, not as rods but as cylinders that do not required end-to-end counting but continuous counting, providing one can count!

#### Angkor Wat as west-facing observatory

I have been doing work on Angkor Wat, something I never got around to after a first introductory post about nested squares there. Both *Lords of Time* and *Language of the Angels* were to have included it. Eleanor Mannikka, spent 20 years on a numerical analysis of its architecture and there is an amazing set of French plans by G. Nafilyan. I looked at the temple as an observatory, since it looks west as aligned towards the sun and moon setting on the horizon, which appears to have been part of its intended use. Settings are easier to work with that risings, since there is plenty of warning of settings as sun or moon slowly travel every day towards the western horizon.