Lesson 3: Making a circle from a counted length

this lesson is in development

The number of days in four years is a whole number (1461 days) if one approximated the solar year to 365¼ days if using a small counting unit like that found across the Manio Quadrilateral (point N to J). It is an important reuse of a four-year count to be able to draw a circle of 1461 days so that this period of four years can become a ouroboros, a snake that eats its own tale, because then counting can be continuous beyond 1461 days

A rope of 1461 inches would be divided into 4 equal parts to form a square and from that, an in-circle to that square that has a diameter equal to a solar year of 365¼ days.

Figure 1 A general method, using the equal perimeters model, applied to a 4 solar year day count of 1461 day-inches as found at the Manio Quadrilateral.

The next step is to draw a circle that is 1461 day-inches in perimeter since (we knowexplain), its diameter will be 14 long relative to the in-circle diameter being 11 long. For this, the solar year rope needs to be divided into 11 parts which can be done by forming a short rope of length 363 at an angle to the diameter. The rope can be marked using a short yard of 33 inches since 11 x 33 = 363 inches. The start of the new rope can be linked to a stake at the start of the diameter and the other end of the 363 inch rope of the new rope can be staked above the end of the 365¼ day diameter and stakes placed along the 363 inch length where previously marked.

However, all that is required to find is the unit length on the solar year rope, which is 1/11th of a solar year long. The lines between the end linkage and the next line will give this, providing the second linkage rope is parallel to first linkage rope (Thales theorum but before Thales was born).

Figure 2 Division of the in-circle into eleven equal parts so as to extend the required radius rope of 5.5 units to 7 units and a diameter of 11 into one of 14 units.

To illustrate, figure 2 constructs a 11-square rectangle, side length 33 inches and 363 inches long. The 33 inch sides are then elongated downwards to divide the 365¼ day-inch diameter into the required units to achieve a circle of equal perimeter length to the square with side 365¼ day-inches. A radius rope from the center can be made of 7 of the new units, long. This enables a 1461 inch perimeter to be inscribed.

This novel application of the equal perimeters, rescued from Victorian textbooks by John Michell and applied by him most memorably perhaps to Stonehenge (in Dimensions of Paradise) is a general method for taking a counted length and reliably forming a radius rope able to transform that counted length into a circle.