Extracted from my second book, *Sacred Number and the Origins of Civilization*, chapters 3 and 4.

#### from Chapter 3 …

The units of measurement in the ancient science of metrologyThe application of units of length to problems of measurement, design, comparison or calculation. specifically relate to the size and shape of Earth. Metrology began with the derivation of what we now call the English footThe standard prehistoric foot (of 12 inches) representing a unity from which all other foot measures came to be formed, as rational fractions of the foot, a fact hidden within our historical metrology [Neal, 2000]. from the equatorial circumference, as well as from the recognition that the mean Earth radius can be perfectly expressed as 7 x 12^6. This model is almost identical to the international models used today for the navigation and mapping of the planet. However, modern science measures things as found and not within a created scheme or order, which was the ancient approach.

This system today would be called a model of reality. Such a model has validity as either a plan from which something is built or an approximation to something real, which can be used as a proxy for the real thing, within calculations. From the standpoint of numerical creationism, the ancients might have viewed their model of Earth as the actual plan according to which Earth’s rotation and hence elliptical forms were organized, or it could simply have represented their discovery of order in the shape of the planet, itself an astounding revision of their supposed capabilities and interests. The main point is that this ancient model, 1 employing rigorous ideas of numerical harmony, indicates a need to model the shape of Earth.

### THE MEAN AND PI

A true model of Earth needs to express the amount of polar flattening caused in the actual Earth by its rotation. Mean Earth dimensions express Earth’s size as it would be if it had not been deformed by its rotation. Both the mean Earth circumference and radius (the distance from its center to its circumference at the equator) have significant relations to the polar radius (the distance from Earth’s center to either pole) (fig. 3.1). For the mean circumference, this involves another approximation to 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., namely 63/10 or 6.3 (that is, pi = 3.15). While 63/10 is not a very accurate pi, the consequence of 63/10 is that if the polar radius is ten units long, then the mean circumference is sixty-three units long. This is a very simple yet surprisingly accurate relationship, one that enables the model to be easily remembered and simple calculations to be performed. This simplicity also makes it easy to use in monumental representations of Earth, as indeed it was in ancient monuments and landscape temples.

#### from Chapter 4 …

#### Ancient Theme Parks

The ancient model described in chapter 3 leaves us with five key lengths, all having numerical components that contain the prime numbers two, three, five, seven, and eleven, when expressed in English feet. These are the lengths of:

• the polar radius

• the mean radius

• the equatorial radius

• the circumference of the mean Earth

• the circumference at the equator

Ancient monument builders, almost without exception, encoded the relationships between two or more of these dimensions of Earth within the dimensions of a monument.

Megalithic examples are found in the Great Pyramid, the lost Tem- ple of Solomon, a number of British landscape triangles that relate to Stonehenge, and the dimensions found within Stonehenge itself. It is very difficult to conceive that this widespread occurrence of the same ratios and metrological system could be an accidental property of megalithic building.

#### AN INTRODUCTION TO SQUARES AND CIRCLES

There are two important ways in which squares and circles can interact. The first is to enclose one within the other and the second is to draw both with the same perimeter length (see fig. 4.1). A square can enclose a circle, touching only at the middle of the square’s sides, or a circle can enclose a square, in which case the corners of the square touch the circle. When a square and circle have the same perimeter length their relation- ship is described as “squaring the circle.”

Construction of a square that “squares the circle” became a sign of geometric wisdom. We shall see that it is the operator pi that effectively governs such a relationship, as pi is the cosmic constant of translation between linear (“in a line”) dimensions and radial (“rotating about a point”) or angular measure. The issue behind such sacred geometrical facts is that the eternal world appears as orbit and rotation, in contrast to life within Earth’s space that operates in linear measure. These two types of measure are extensive and intensive: linear measure extends a dimension, while angular measure divides the whole that already exists,

making the whole more intense or meaningful. In this way, the meaning of circle and square within the mind of the sacred geometer quite probably come with all the baggage of eternity versus existence—a dualism that offers a path of knowing through the study of geometric behavior.

If a circle of diameter one is inscribed within a square, then the square will have a perimeter length of four, while the circle will have a circumference of pi (fig. 4.2).

The difference between four and pi is easier to see using the anciently favored approximation to pi of 22/7The simplest accurate approximation to the π ratio, between a diameter and circumference of a circle, as used in the ancient and prehistoric periods. (3.142857 is 99.96% accurate).

4 – 22/7 = (28 – 22)/7 = 6/7

This difference in perimeter can be expressed as a circle with a diameter 6/7 times 7/22. The sevens cancel to leave 6/22 as its diameter, which simplifies to 3/11 of the original, inscribed circle (fig. 4.3).

This ratio of 3:11 is exactly the ratio between the Moon’s diameter (1080 miles) and the diameter of the mean Earth.1 From this we can see that the Moon represents the difference between an inscribed circle and the square that encloses it, by having a circumference that is the difference between the perimeters of the inscribed circle and enclosing square.

The baggage associated with this simple but cosmic geometrical fact is that Earth represents a sphere of materiality, and things material are symbolized as being square. The Moon is therefore, symbolically, that which materializes Earth from an eternal circular form into space. Whether or not one wishes to enter into such a symbolic meaning, the bare fact that the Moon, originally projected from Earth, came to possess just this pi dimensional relationship implies there were extraordinary influences at work in its creation.

Placing this 3/11 Moon circle so that it just touches the mean Earth, it can be rolled around the greater circle in what was called the “sublunar orbit.” This orbit demonstrates the second relationship of square to circle called “squaring the circle.” The circle created by the center of the Moon as it is rolled around Earth has the same perimeter as the square

## THE PYRAMID, PI, AND THE MOON

This ratio between the diameter of the mean Earth as eleven and the distance between the centers of Earth and the Moon as seven is the exact ratio built into the Great Pyramid of Giza (fig. 4.5). Eleven over seven is the relationship of a radius to a quarter sector of a circle, and in the case of Earth, a quarter sector is symbolic of the distance between the Pole and the equator.

images and text (c) 2007 Richard D. Heath, sacred.numbersciences.org